So you will need to do the boost within 30 days of the transfer.
I have boosted BA Amex sign up bonuses and credit card spend avios, never tried MR but I presume it shows up in the same way as the bonuses do.

If you transfer avios points from Iberia or Qatar etc Or have them gifted to you by someone else, I suspect you will not be able to boost them (otherwise you could go round in a loop).
I can't remember if my Sainsburys points converted into avios were boostable as well. Might be because you lose out if converting one way and then back again which you don't with avios-avios transfers.