Using an HD 600 to play video games on my PC

I want to be able to hook my PS2 up to my PC and play games on my monitor and stream them using OBS. I found an ATI TV wonder HD 600 

http://www.newegg.com/Product/Product.aspx?Item=9SIA10V1Z55025&cm_re=ati_hd_600-_-9SIA10V1Z55025-_-Product

That one to be exact. So i would like to know if that would work and if there will be much controller lag using this set up.

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