It is possible, yes.
If you are pledged to either the Empire or Federation and you kill members of other powers of the same faction, you will get -30 merits for the kill.
As an example, if you are Pledged to Hudson, and you kill NPC's that belong to Winters, you will get the negative 30 merits fine.
It is possible, then, that if you kill enough NPC's, you will end up with a negative Merit balance.
Since the Alliance only has one player, Mahon, it is not possible then to end up with a negative Merit balance if you are pledged to him.
I am unsure if the same applies to the Independent Powers.
I also do not know what type of impact a negative merit balance will have at cycle changes. But I cannot imagine it would be in any way beneficial to have a negative balance when the cycle change happens.