No, because if you have a room empty, you now have to identify the vacated room, which could take an infinite amount of time

Also, it would take up to an infinite amount of distance to walk to or from the front desk, so we just be dealing with immortal guests who have no time sensitivity at all

Furthermore, the room must be made ready and guests tend to check out at a certain time of day, so you would have to decentralize everything while accounting for light speed limiting the speed of information

Some of these problems are solvable if you add more constraints to the puzzle. Like, if you have a rate of check-in to checkout you could do something with statistics and discrete math to divide the infinity into an infinite number of sub hotels, and in doing so possibly guarantee availability for the guest in a long but linear amount of time

It would be an interesting programming/math puzzle. My intuition tells me it is solvable, but it might not be