Is it okay to freeze a cheesecake for a shorter period of time as opposed to chilling it longer?

Don't freeze it. I tried that. The ice crystals that form at the lower temperature make the cheesecake texture awful and can cause cracks.

However, people will eat warm cheesecake so just chill it in fridge for whatever amount of time you do have.

I wouldn't freeze it, especially if you're planning to serve it at a party (and thus wouldn't want to risk a failed experiment). Likely, the outside of the cheesecake would freeze but the center would remain warm.

If you haven't made the cheesecake yet, you could try making small individual-sized cheesecakes (in muffin tins, perhaps). If it's already been baked, and there's no way to chill it for the recommended time, I would go for a Plan B.

A few cycles each in the fridge and freezer might help, if you're careful, and lucky. You should probably still have a back-up plan, if it doesn't work. and be prepared to keep the cheesecake for yourself if it doesn't end up quite right.

You will want to avoid freezing the cheesecake - as Ammnar Naseer said, that can affect the texture negatively because of the ice crystals that form. But what the freezer can do, especially in the very beginning, is cool the cheesecake more quickly. A few short sessions in the freezer will get it drop the temperature down much more quickly - but you will want to aim at fridge temperature, not a frozen temperature. Letting it sit in the fridge between sessions in the freezer will give it time to equalize the temperatures, so the middle will cool before the outside freezes.

I would not go longer than 10 or 15 min at a time in the freezer, and at least the same in the fridge between, generally. Maybe it can stand a little longer the first few times, when the temperature is still obviously above chilled, but shorten the cycles the closer your cheesecake is to reaching a refrigerated temperature. So using the freezer will buy you a bit of time, since the first part of chilling - getting the cheesecake down to fridge temperature - will go much more quickly for periodic exposure to a much cooler environment.

What it will not do, and might interfere with, is speed up what the rest of the chilling was supposed to do. This means whatever benefits come from resting at a refrigerated temperature, while the cheesecake slowly comes together, or the flavors meld, or the moisture equalizes, or whatever chemical thing that means a 12-hour resting is better than a (say) 4-hour one. Whatever that reaction is, it will probably happen slower at colder temperatures. It might happen faster at some temperature higher than the fridge, but probably the longer time is a good tradeoff for a safer resting temperature.

I'm drawing from this question which notices the difference between a four-hour chilled dough, and an overnight one. One set of time (I'm using the four hours from that question, but it will vary) is how long it will take the cheesecake to cool down. The other set of time is how long it will take to finish reacting once it is cool.

So, assuming you can use the freezer in a couple short bursts in the beginning to bring the temperature down to cool without leaving it too long and being frozen, you might shave several hours off the time needed in the fridge, and spend whatever time you have left resting at temperature as much as you can afford. Maybe that means you're heading out with a cheesecake chilled equivalent to 8 hours instead of 4 1/2. That is still less than ideal, but it may be better than you could do otherwise... and if you still don't like the looks of it at that point, or if it got accidentally over-frozen at some point, you can leave it to finish chilling for the next day while you take your backup plan.

Short answer use convection. Use a small fan beside the cheesecake in the refrigerator blowing horizontally over it(covered of course). This will result in the cool air pulling the heat away from the cheesecake. It should decrease the cooling time by roughly 30-40% or by about 4 hours on a 12-hour chill time.

Cheesecake "blooms" overnight or at least 8 hours in the refrigerator. It becomes thicker and has that cheesecake thickness with tiny pockets of air that make it so heavenly and creamy. I have never been able to get that quality without letting it sit for a long time in the refrigerator. Fast cooling just doesn't let it set and bloom.

I've read that you can freeze already baked cheesecakes and have even made a recipe that called for directly taking the cheesecake from the oven and putting it into the freezer until the rest of the components were made. After the cake was assembled you allow it to finish resting in the fridge. It was delicious. I had no problems with ice crystals forming and had actually forgotten about it in the freezer for a few hours. I tried the recipe another time but skipped the fridge portion and the cheesecake didn't set. Cold on the edges and room temp and not tasty in the middle. Getting the cake to cool to it's core is key. I think if you freeze the cheesecake then just allow enough time to thaw in the refrigerator.