I think it will slow the polls down if you have to go to the effort of joining the poll site rather than just clicking a button.
It probably will at least a little. But it's wishful thinking that it'll do away with them to the extent (presumably) desired.
Two reasons:
1. Prohibition never works. The moment you prohibit something that has demand, a black market appears. The more draconian the enforcement, the more lucrative the black market becomes. Black markets are pretty much always a worse thing than having things handled above-table.
In the case of the forums, mods here could go whole-hog and say posts with external polls are banned, but I don't think the reaction to such a draconian measure would be pretty.
2. Gamers are, by & large, fans of problem solving by nature. No sooner had forum polls become unavailable, than 3rd party site polls and petitions on change.org & such started to appear.
One way or another - they will find a way. Again, unless there's an outright ban on polls, and an ensuing battle between dwellers & mods, which would be an ugly turnout.
If I would suggest anything would help at this point, it's some quality control. I'd hazard that the recent spate of poll spam came about from following FD's own example (albeit inadvertently) with the delayed ship transfer thing. Ball is in their court now to set the example of what polls should be used for / how to do a good job of constructing them, rather than trying to snuff them out using controls that'll only have partial effect.
But that's not for me to decide

the community team have my confidence. The boards are very well managed imo. Just sharing my two cents is all.