I wouldn't use the verb "stocker" for baggages. it's better "déposer"
bags or luggage could be said "stuffs" too.
Puis-je déposer mes sacs à l'avance?
À quel moment puis-je déposer mes bagages? (or maybe better, more "every day talk" : Quand pourrais-je laisser mes affaires?)
vous les gardez combien de temps? (how long do you keep them?) they probably keep them as long as there's someone physically at the hotel's reception, so look for any reception time range information
Note that France French and Canadian French are not always using the same words.
it's not a mistake, just not usual.
fall in love :
in france : tomber amoureux
in quebec: tomber en amour <-- nobody would say that in france.
In france the verb "Stocker" is more used when you are placing something in a place for a very long time (days or months or more). Not temporarily.
I don't know if quebec is using it more often for every day use as "deposit" verb.
you could also use the verb leave instead of deposit.
Puis-je laisser mes affaires avant d'avoir la chambre ? (can I leave my bags before getting the room?)
Je pourrais laisser mes affaires avant d'avoir la chambre ? (I will be allowed to leave my bags before getting the room?). That may look awkward, but this form is less formal and more used for every day speaking.
I think it's better to specify "before getting the room" if it's what you want to ask. leaving your bags the morning for example, but the room can only be accessed the afternoon. so you ask if you can leave them at the reception before getting the room.
For the second sentense: "À quel moment puis-je déposer mes bagages?" could become
"Quand puis-je les laisser?" (when can I leave them?) (no need to repeat the luggage/bags/stuff word, we now know we are talking about "them").
or "je peux les laisser à partir de quelle heure?" (I can leave them at which time?)
You can probably leave them to the reception at opening hours (8-9h?), when there's someone there. look at the opening hour range.
For the first one: the time you can go to the room. (if the hotel is registering before you can access it)
La chambre est libre à quelle heure? (unformal form) (the room is free at which time?)
A quelle heure la chambre est-elle libre? (formal) (Which time the room is free?)
French (and probably a lot of languages) have many ways to tell the same thing. Different words or sentence formation. "I can go?" "can I go?" "may I go?" etc. lot of nuances.