I had this happen the other day with KDEN. METARs all morning were reporting 1/4sm-3/4sm RVR2000v4000. TAF called for it to clear after 18z and my ETA was 1950z. The PIC called about it and we both agreed that it was out of the 1-2-3 rule for requiring an alternate. They departed KORD enroute to KDEN, I'm just sitting there watching the METARs remain unchanged while my flight draws closer. Seeing as how the NWS is notorious for chasing METARs (no pun towards those weather folks out there), about an hour out I went ahead and added KCPR as the alternate just in case something did happen even though all the flights were getting in. Of course they made it in ok.
To answer your question, I look at it this way. Since our paperwork is due 1 hr before ETD and it is forecast to be good when the paperwork is sent, no issue. If it changes to require before they push, I advise to withhold the push and call for more fuel as I'm working the numbers to add an ALT. Otherwise once they push and under their own power, the paperwork is legal. Keyword here: under their own power. (But I still keep a plan B up my sleeve just in case)