Absolutely. Also the TOS crew didn't have 'direct' communication with Starfleet command, and on several occasions part of the drama is that it could take days for Kirk's communiques to get to them and a further few days for a response to make its way back to the Enterprise, in which time Kirk still needs to deal with the problem at hand.
For some reason, it seemed that whenever they were out of direct contact with Starfleet, the response time was always three weeks. Well, not constantly, but a figure of three weeks or more was specifically cited in "Return to Tomorrow", "The Enterprise Incident" and even TAS: "The Time Trap".
Now that is
interesting. That does make one wonder if even the Constituion Class Enterprise was often no more than a certain distance from Federation space? If the three week thing is a measure of how far away they are from 'home'.
Of course, Roddenberry always said he didn't like the idea of the Enterprise reporting in to home or visiting Earth. It's somewhat ironic that most of the TOS movies revolved around trips back and forth from Earth, rather than anything resembling "exploring strange new worlds".