Not necessarily. It could be they initially rechristened a Miranda class (
USS Enterprise NCC-21701) and used it as an academy training vessel through the 2350s. The training ship just happened to be retired in the early 60s and Starfleet re-appropriated the name for a galaxy class starship in honor of the crew of the 
Enterprise-C. 
 
	
	
		
		
			Unfortunately that theory doesn't work, as the dedication plaque for the Ent-D states "Fifth Starship to Bear the Name," regardless of what the registry number was.
		
		
	 
		 
 
Technically this could work if the vessel was either not in Starfleet (but was a Federation vessel), or was not considered a starship due to her assigned/designed task not being in line with what a "starship" is used for.
 
A training hull that isn't really given a standard hull number. Something like say the 
USS Sable in World War II. A coal powered, side wheeler aircraft carrier that was built from a Great Lakes excursion steamer to be a training carrier on the Great Lakes along with the 
USS Wolverine. These are not proper carriers in any light. They are more or less just moving flattops for training pilots how to land and take off from a carrier at sea. These used the "unclassified" designation in the Navy books. 
Sable was IX-81 and 
Wolverine was IX-64.
 
Sailing ships 
USS Constitution and 
USS Constellation also used this numbering system as IX-20 (
Constellation) and IX-21 (
Constitution).
 
So take an older Miranda-class ship, an Excelsior, or even a really old 
Constitution hull. Rename it 
Enterprise and give it some odd registration number, and there is an Enterprise in existance between the loss of 
Enterprise-C and the commissioning of 
Enterprise-D.
 
This ship can have its name changed to something else later on to free up the name Enterprise for a new Galaxy-class ships. This has also happened before. During the early 1920s, the 
USS Constitution had her name changed to "
Old Constitution" to free up the name Constitution for a new battlecruiser. The Washington Treaty cancelled that battlecruiser (her sisterships 
Lexington and 
Saratoga would be converted into aircraft carriers and begin the naming convention of carriers after old battles instead of famous aviatiors and aviation sites as was the plan following 
USS Langley). Following the cancellation of the battlecruiser, "
Old Constitution" got her name back, and was refurbished for a tour around the coastlines in the early 1930s. 
USS Constellation was removed from the Navy registry and placed as a museum ship to free up the name for the carrier 
USS Constellation (CV-64) in the 1950s. Also in the US Navy, sometimes ships get downgraded and renamed to free up names for larger or more important ships. Around 1900 there were a number of Armored Cruisers that were named after states just like the battleships. 
USS Pennsylvania (ACR-4) was a famouse one for being the first ship to be landed on by an airplane. This same ship was remained 
Pittsburg a year later to free up the name for a new battleship (BB-38). All of those class of ships were renamed in favor of new battleships. Even the first battleship 
USS Texas was renamed so that a new battleship 
Texas could be named.
 
So there is the possibility of a 
USS Enterprise between ships. Just not one that is actively doing regular Starfleet missions.
 
One example that comes to mind is the ship from the fan film "Of Gods and Men". The 
USS Enterprise (NCC-1701-M) museum ship. A Constitution-class vessel fitted out like Kirk's ship in the 2260s, but with later era safety features required by Federation law. Another example would be some sort of warp test hull used to preform experiments with a new drive engine for the Galaxy-class starships. Something like the NX-class in purpose, but not used for exploration work. Just for testing the engines and maybe some other systems that would later be fitted to 
USS Galaxy for more intensive field testing.
 
Or something even more odd. Something like a captured Galor-class ship being used by Starfleet for some purpose renamed 
Enterprise by some Admiralty. The name being "unofficial" like 
HMS Bounty was an unofficial name for the captured Klingon Bird of Prey by Doctor McCoy.
 
Or even something like a Federation survey ship that is not in Starfleet, but one of the other departments.
 
EDIT:
 
Additionally, on this same thought, what if the 
Enterprise-B was downgraded when the Ambassador-class was coming out. Someone on the Council or Admiralty wanted the newest exploration vessel to be the "Enterprise" but the Excelsior-class 
Enterprise was going strong. Someone decides to rename the 
Enterprise-B to something else so the name can go to the 
Enterprise-C. The older 
Enterprise-B remains in service is some capacity, but with a different name. And that does happen in history. The earlier mentioned USS Pennsylvania stayed in service as the 
USS Pittsburg until 1931. This overlaps with the service of the later battleship 
Pensylvania by almost 20 years.
 
Now imagine if the 
Enterprise-B was still in Starfleet, but with a different name, when the 
Enterprise-C was destroyed in 2344? Would it be possible for them to rename the ship back to 
Enterprise, with its old registry number, until removing it again when the Galaxy-class 
Enterprise is ordered? Or is that basically impossible since depending on when the 
Enterprise-D was ordered.  What if the 
USS Lakota is the 
Enterprise-B and only one of that style was built (note that is highly unlikely).