Yes, modern pc's are very energy efficient. Consider stepping up to a 500 or 550 watt if you might add a video card in the future. Just make sure it has enough physical power plugs for your SATA (hard drives) devices.
I know the 1050 does not need any additional power, but the 1050ti does need a 6-pin PCIe power plug. Check the manufacturer's website, or look at the card itself.
If it has a plug on the card, you'll need it for sure. Most power supplies have at least one.
While it may work I wouldn't recommend that PSU with that GPU. It's one of the lowest quality Corsair PSU's out there and your PSU is the heart of the system. If you can get the CX or CXM Corsair over that VS.