I don't know the rules, but I think you can. I think is is like with final ę where some Poles pronounce final ę and some don't.
I "suffer" from hypercorrection of speech, I do pronounce ą and ę too clearly in many people's opinion, but even I wouldn't go with zaczełłam or zaczołłem. That would sound ridiculous.
I meant ę not eł. of course zaczełłam sounds silly, but you can say zaczęłam a bit more nasally than poseł. But also you can say both the same. And I have no idea which one is supposed to be "the more correct" one.
But of course I guess non native speakers would probably be better with just eł