No – unless you specifically requested it in scope of instructions, it is not the responsibility of the conveyancer to obtain a copy of the management agreement. It is up to the purchaser to make their own enquiries. Of course the purchaser can ask someone to do that for them, but they have to specifically ask. In a conveyancing scenario the primary concern is whether you are getting good title.
If I were you I would get a strata lawyer to have a look at that management agreement, I bet they could find a number of holes in it.