If you were to get a skill boost from one of the God blessings, and it takes you to the point where you would qualify for the Master rating, would you be able to do the master quest?

EG If you got Velorien's blessing (Ultimate blessing) which, among other things, increases melee and dodge by 12 and you had enough invested in those skill that the count takes you into master territory, could you do those quests?

Also if you get the Ultimate blessing, can you supplement it with one of the lesser god blessings? ie make an offering to one of the basic gods to increase the buffs you have ?

The short answer is yes. Make sure you have enough of the requisite stat (in Dodge's case, DX) to get your stat bar up to at least 4-and-a-fraction points in the skill.

Also, a protip: the Dodge and Melee quests are best done together, because the masters involved have a history. For the best result, don't complete one without starting the other. This is a hard no. If you go back to the first altar after receiving the final blessing, it will refuse your offering. You don't get to have your cake and eat it too.

Thanks TwoHandedSword, I figured that that was probably the answer in both cases but it's nice to have confirmation.

And yes, I did know about the melee/dodge connection; that's actually part of the reason i wanted to know. My current character isn't melee focused but I do like to do it if possible as i find it one of the more interesting side quests, mainly because of the masters' history.