I did some extra testing:
If I send an email using Gmail's standard interface, an extra "No Virus" signature is added to my email.
If I send an email using Gmail's simplified HTML interface, no extra signature is added to my email.
It gets more complicated when I reply to an email using Gmail's simplified HTML interface. I got the HTML tags signature to show up when I turned on the "Include previous messages" option, and I made it disappear when I turned off the "Include previous messages" option, but while I was retesting just to be certain, I couldn't manage to get the HTML tags signature to show up. So I'm at a loss for words.
I'd say if you can, keep the signature when an email is sent in Gmail's standard mode but leave the signature out from Gmail's simplified HTML mode because the signature does not render properly in that mode.