Is there any implication/consideration for using the boost module on many different websites running on the same VPS? Is there any implication/consideration for using the boost module on many different websites running on the same VPS?
Boost has options for how you structure the files, you can use the ip address or the host name. 

In your case you would want to stick to the host name so the files are separate. Other than that I see no reason why it shouldn't work. Though I haven't tried.