Good question - which I just modified the FAQs post to include.
The answer is basically no they don't really do status matching unless your company just switched to National for their contract rates (in which case you'd have to contact your travel people for them to contact their National rep to give you status).
However, they don't match status on individual basis. Sounds like Avis First is an invitation only status for heads of companies or those with a lot of influence on corporate travel - this should be equivalent to National's VIP "status" which is above Executive Elite (highest published level). You'd start off at base Emerald Club level (which still allows you to pick your own car but selection isn't very good). After 12 rentals (in a calendar year), you'd be Executive with access to Executive Selection (better selection).