The purpose of a UPS is to be able to provide sufficient power in the event of a power outage to be able to save your work and do a graceful shutdown. As you mentioned, it's doubtful that your 1200W PS will be drawing the full amount but, if it is, the result will be that the 750W UPS will only be able to maintain your system for approximately 63% as long. What that means is if the 750W UPS is specified to be able to provide 10 minutes of up time, it will only be able to provide about 6 minutes with a 1200W load.
BTW, you really need to take into account more than just the PS rating unless you only plan to plug your CPU into the UPS. What about your monitor, powered speakers, printer, etc...?