SOME models of the 1050 ti only use slot power. SOME models DO require supplemental power.
Regardless, unless you have the best 240w PSU ever made by any of the actual key PSU manufacturers, then no, a 240w PSU is unlikely to be a trustworthy configuration. Especially considering that there are OTHER components like drives and the CPU which also need power and chances are EXTREMELY good that you have a really poor quality unit since there are very few high quality ATX form factor power supplies available in that capacity.
Further though, knowing the EXACT model number would be key to determining this for certain. If it is an OEM PSU that came with a prebuilt unit, and unless it is a Delta or Seasonic built model, then chances are very high that it's more of a PSU shaped object that a reliable power supply.
The EXACT model number should be printed on a label somewhere on the back or one of the sides of the power supply. Relate that model number to me and I'll offer you a more informed opinion on whether or not it's even remotely feasible that you should rely on that for your graphics card or not.