Well Chekov does ask for a "photon torpedo load status" in TMP prior to departure to intercept V'Ger. He could be querying the computer, but since nobody else asked the computer questions during the film, he might very well have been calling down to the torpedo room to ensure that the crew had both tubes loaded with shells.
I've often wondered that too. That Chekov dialog was in the pre-Director's edition I believe (I could be wrong, but I think it has since been cut, though I still hear it in my head every time the movie plays.) About asking the computer questions however, there was at least one example. When Kirk visits Decker for the first time, there is an engineering checklist bantered back and forth between a female crew member and the masculine computer voice. This too has been excised from the Director's edition I believe. (That cool computer voice was completely removed from the film)
Chekov could have been inquiring to that computer persona though we never hear a response (from a computer or a crew member.) As to the load status of the torpedoes, they could be simply referring to the loading of the torpedoes onto the ship in stockpile rather than any primed or armed status. The ship was about to leave dry dock for the first time in 18 months and they were in a hurry. I think they mentioned the torpedoes in that sequence specifically because they intended to use them later in the wormhole sequence. Decker would later order, "Arm photon torpedoes" and that took place lickety-split. That indicates auto-arming is a very fast procedure or that the torpedoes were already close to their launch port, unlike in TWOK. I also agree that the TWOK crew's "hands on" torpedo approach was the result of the ship's status as trainee vessel and the severe damage they took in the first attack.
So Chekov's dialog could be at any stage of the torpedo loading for all we know but it is a neat clue, if one's version of the movie still has it included.