No.
Once a car has been imported to the UK an application is lodged with HMRC and car is placed on their NOVA database and a certificate issued.
This is confirmation the correct duties and import VAT have been paid.
DVLA cross-check against the NOVA reference on all new ' first registration' applications.
No NOVA = No registration
A 'Q' plate is only issued for vehicles on which the date of manufacture or first registration cannot be proven, sometimes the overseas registration document is incorrect or missing, hence the occasional need for a 'club dating letter'.
Another point to be careful with on South African imports, occasionally it may say on their registration certificates ' Built Up '.
This may just mean the car was off their registration system for a period of time (quite common with old cars as may have been taken off road for restoration or laid up etc) but DVLA in their wisdom automatically assume this means the car was previously written off and must therefore be dodgy. They will flag it up and then you have a real battle to prove otherwise, club letters mean nothing in this scenario. If you're lucky and you get a nice clerk looking at your papers they may send an inspector out, if you get a jobsworth whose cat has just been run over, you face an uphill fight to avoid a 'Q' plate.
Here endeth today's lesson Woody, no charge
Homework over Easter - What do I do if my car was manufactured outside South Africa and sent over CKD for local assembly ?