As stated earlier, the offence is "failing to display a RFL"... You CANNOT be convicted of failing to display something you don't have.... The offence was to ensure people displayed there RFL correctly when they were checked by enforcement officers, this was before the advent of the computerised system of checking if vehicles are taxed. The serial number of the tax disc was used to positively identify your car in parking infringement cases, so they had to have them displayed properly, they now use cameras.
No RFL and failing to display are dealy with by the DVLA, when/if a policeman/traffic warden fills out a form and forwards it on it ends up at the DVLA. By the time it gets there you will have taxed the car, as long as there is no gap in the taxation then no further action will be taken against you.
The DVLA are a tax collection agency, they are not interested in wasting money prosecuting you if you have paid your tax....
Above is how it SHOULD work, you will always find horror stories of DVLA etc making a right mess of any aspect of tax collection....
If you have sent the forms off and are waiting on a responce from DVLA then just use the car....