... AND he had a Beagle. Which makes it likely that it is the same Archer, but not definite. Archer is not an uncommon surname, after all, and the popularity of beagles as pets for Star Fleet personnel is something that none of the series or movies have ever addressed.
Offscreen assertions of production staff aren't canonical, and it's unlikely that a man born in the early 22nd century would have that kind of life expectancy. I personally think Admiral Archer is more likely to be a son, daughter, or other descendant of Jonathan. Preference in pets can easily be handed down from one generation to the next.
And I guess for that matter, the Battlestar Galactica arrived at Earth sometime before the 23rd century, as I also recall seeing Colonial Viper schematics being shown in that same scene on the library computer.
^^ I was not aware of any Colonial Viper schematics in the mix? In any event, this would fall into the category of "in joke" which need not be taken seriously, as per my previous post to the one you quoted.
^Or maybe not an in-joke, maybe just a case of grabbing whatever was available that would suggest "spaceship schematics" to the moviegoing audience. They weren't making the movie for the benefit of fans decades later who'd go over the home videos with a fine-tooth comb and obsess over trivial details. They were just using the resources at hand to convey a general sensory impression to the folks in the movie theater.
^^^ I'll have to dig up some screen caps. It was around the same time that the "Official BSG Blueprints" came out (78-79) and would make sense that they would be available and used for random background flotsam. The attention to technical detail didn't really seem to exist back then in the way that it does now, and they certainly never would have predicted that, 30 years later, we would have access to hi-def BluRay/DVD sources to nitpick the color of wall-pixels.
Or that the Enterprise D's sickbay has a "Medical Insurance Remaining" display. Wait -- there was a duck? Where?
^^ In TNG's timeline. Obamacare is still in effect. Likewise there's no money in the TrekUniverse because once the debt hit 1 quadrillion dollars. They just did away with it. Nothing to balance.
In the original MSD, there were a bunch of little silhouettes hidden throughout the diagram, one of which was a rubber ducky. I think there was a Nomad probe in there, too, along with some other weirdness.
Do we discount the dedication plate on the Enterprise Dee, which lists a Admiral Gene Roddenberry? Well, the Defiant could have been from a different universe, than the TOS Defiant from The Tholian Web. Lots of universe's out there.
Speaking of taking on-screen evidence from freeze frames too seriously, Memory Alpha contains a heated discussion with a large number of people insisting that the Soviet Union was revived in the 24th century.