It's not just as simple as will it or wont it work im afraid mate, you will need to check your power supply, although some psu's say 750w they may in fact not output that high. Also the 560ti requires a minimum of 30A on the 12v rail. If your psu is not outputting this then it will not sufficiently power the card and could cause system instability.
To check the power output there is a grid on the side of your psu, it will say 12v then under that tell you what the output is.
Also what brand is your psu? as the basis for any good reliable system should always be a good psu