Can I run 2 non thunderbolt monitors off a 2013 13" Retina Macbook Pro? One connected via HDMI, and one connected via a Thunderbolt to HDMI adaptor?
And if so, can I also run the laptop screen at the same time?
Yes, what you're suggesting will definitely work and you can use all three displays at once (MacBook display + HDMI display + Thunderbolt/HDMI display). This is the Mini DisplayPort to HDMI adapter that I personally use and recommend.
Certainly the two external monitors will work and although I haven't tried it, the internal display should still function since it's not listed as being dark like on the lesser Macs here where connecting an external causes the internal to be dark intentionally.