And what is the potential impact (other than many Democrats not having a say in their own candidate) of a legitimate campaign to try to convince Democrats to do so?
No it's not a realistic plan. It would require massive coordination in multiple states, which would be apparent and make their own primary more susceptible to a similar attack. This would be viewed negatively by large portions of the country; sinking a particular opposing candidate is more important than selecting a quality candidate of their own is a bad message to send. The GOP could simply change the rules in the face of such an attempt, depending on how they did this and how apparent Democrat interference was Republicans may not even see any backlash for changing the rules.
Any candidate that could be chosen on the Republican side would still be someone the Democrats don't like, they would be a somewhat popular Republican. Such an action of outright disenfranchising of Republican voters in their own primary would create a lot of sympathy for them and may cascade to a Republican victory in the general election, which would be a defeat for Democrats anyway.