I would transit to IFR as the zone boundary i.e. pretty well right away. But one won't get an RIS if below the minimum authorised RIS level for that radar unit, so in the conditions described one would be IMC by the time one gets any cover.
We don't lay down a minimum altitude for RIS, only RAS. At lower levels away from the radar head (1000ft per 10nm is a good rule of thumb for lower limits of cover) the service will be limited and the reason for limitation will be explained in the 'verbal contract' of service.
What I don't know is whether the PILOT himself is able to phone the radar unit before departure, and get a squawk allocated.
Nothing to stop you - but I wouldn't bother. There are many standing agreements between adjacent units regarding the verification and validation of squawks. You could end up in a position where you get airborne, wearing this pre given squawk, but your mode 'C' is out. Adjoining unit sees you wearing another units squawk, take it to be validated and verified (which it hasn't been) and promptly has an airmiss with you because the mode 'C' isn't what it appears to be.
Just call as soon as possible.