You should have a good quality PSU, if you could get the brand name of your current PSU it would be easier to know if it's PSU related, also I don't know everything you have inside your Case, how many fans, hds, ssds, etc so the best way to know how many Watts you need to better suit your case components is by using a Watt calc like this http://www.coolermaster.com/power-supply-calculator/. But as by my own experience, I would recommend something around 550W for this spec because sometimes both GPU and CPU depending on the game could consume much more power than normal.
Now regarding your question the boost would be related to your computer not running out of RAM and for improving the loading performance by disk caching and avoiding freezing due to virtual memory swapping which is pretty common to happen and it's basically one of the main reasons for stuttering. You can take GTA V as an example of that, running the game with only 4GBs will cause extreme stuttering after playing for a while, the game uses more than 4 GB and when that limit is almost reached it starts to use the page file / virtual memory.
Now the only way to know who the culprit is by either testing with a better PSU or getting another 4 GB of RAM, if you don't want to buy it straight away, you could borrow from someone you know who has it a good 4 GB stick from a quality brand.
In this case I don't think the PSU would be the problem here because there are only two answers for it.. it works or it doesn't, if your PSU was the real problem your PC would become unresponsive or at least some of these components would (CPU, GPU), also if it was the PSU your PC would turn it off itself while ingame due lack of power or juice. So try borrowing some more RAM.