Not really. If anything, the Quadro NVS 300 has too little RAM to even enable GPU acceleration at all - and that is not to mention that it's even older than the GT 730! Worse, driver support for the NVS 300 already ended way back in 2016!
And why are you looking at anything in the $500 range to begin with? You know that you will need to spend at least $1,500 just to get a system that's even minimally suitable for 1080p work to begin with.
By the way, that PC will suffice for 1080p - but you will need to completely replace the GPU with something newer and more powerful. (In this case, even a GT 1030 with GDDR5 memory would be a better choice than anything that you considered so far.) But that might bring your total to over the $1,000 that you stated as your maximum budget limit.