Yeap, the DVLA will send it back saying no insurance. You need to insure the bike against the frame number which is what the MOT will be against. MSM will not insure bikes without registration. You will have to use one of the big 3 bike insurers who will normally insure a frame number but only for 2 or 3 weeks. They will cancel the policy if you don't go back to them with the registration number within the set time limit.
This link to the VMCC has some good info!
http://www.vmcc.net/media/file/SOS%20form.pdf
You should buy RTA insurance at each road trial as all normal motorcycle insurance policy's (Except MSM) will invalidate the policy if the bike is being used in competition! IE a Sammy Miller round which are all road based trials..........
Do many bother. Probably not!
Link below to MSM Insurance if you want to double check if they will insure for a few weeks on Frame / VIN number as it was some time ago when i last checked and the answer was NO, but things do change.
http://www.msminsurance.co.uk/trialsenduro.asp
Hope that helps.......