You raise common points in misunderstanding the law, but they are easy to correct.
People can simply say they are registered if they have some giant fear like you say and wish to not register. The forms are also required to say that the welfare value won't hinge on it. Also, the office staff are often less than enthusiastic about this program as it requires another form for them to handle. Trust me, there's little risk of coercion here. The issue here is offering assistance with the voter reg form as they would with any other paper work, that's it. No pushing required or asked. In fact, the law is pretty clear on this. Sadly, the law makes the DMV registeration system very smooth and the welfare office one cumbersome. And you're worried about it being biased towards Dems? The DMV aspect of the law has largely registered republicans and independents.
Oh, and what's wrong with Democrats pushing low income and minority people to vote? Why don't you ask Republicans to do more of that???
You are probably correct that public servants avoid doing any more than the minimum (or less) required for their job. And that alone should rule out coercion.
Nothing wrong with pushing anyone to vote, as long as it is done outside of normal government functions.
I believe in individual acheivement and self motiavation, if someone has so little interest in voting they can't send in a postcard to register, I rather they not vote. Given nearly $2 Billion will be spen to promote the candidates and the issues, if people don't see a reason to vote, I don't think government employess should be pushing people to so so (whether they are potential Republicans walking into MV offices or potential Democrats walking into welfare offices).