Sadly the normal blood tests (Liver Function Tests/LFT's) will not in themselves make any difference whatsoever.
dvla only look for negative information, and couldn't care less where it comes from. Your doctors opinion outweighs a metric ton of normal blood tests, and are not interested in fairness/accuracy/credibility, just ticks in a box.
The only use regular blood tests will have is to convince your doctor that you are genuine, because it is their opinion that counts (even if they dont know what dependence is), not the LFT test results alone, and if your doctor can say you have had no problems and can tick that box, AND all the other boxes, AND your
CDT test is good when dvla insist on it, then, and only then, you should be ok.
Just for information, a very severe alcoholic/dependant person that stinks of alcohol on a permanent basis can have normal liver function test results, yet a poor result can be used as "proof" of dependence by dvla if they find out about it, and reset the 1 year abstinence clock.
It's all just bollocks really.