I think it actually tunes to the mux, so theoretically you could watch and record different channels so long as they're on the same mux - all the HD channels are on one Freeview mux in the UK, though, so it'd be 2xHD or 2xSD. That said, I don't think tvheadend supports this function anyway, and I don't know about other backends, so it's academic to a certain extent; I'm sure I've read somewhere that it's possible to dump the whole mux out to disc and then demux it later, but a second tuner is a lot less hassle.
tvheadend is quite happy with multiple sticks, so I'd see no reason why two of the same would cause a problem. Indeed, since you have an HD-capable stick now, you only really need a cheap SD (DVB-T) stick for the SD signals, and then set the priority of the sticks so the HD one is preferred. That'd leave your SD one free most of the time.
I get perfect HD reception on my PCTV 290e, if that helps (Acer Revo R3600, Ubuntu 11.10/Oneiric, tvheadend 3.5.65~gddc466c-dirty off the Ridge Hill transmitter).