Does the Jol-Nar promissory note allow the recipient to research faction technology unit upgrades?
No. The card says "Gain that technology". It does not allow gaining your faction specific variant of that technology. Effectively, this means that you cannot use the card in that situation (or if you did, it would not get you any benefit).

I don't have an official ruling to back this up, but a literal reading of the card text seems pretty clear. This thread on BGG agrees.