I think they would be delighted to have a suit pending while he is the candidate, and should he be elected, to be dragging on casting doubt over the validity of his Presidency.
As far as comments that Dems would prefer Trump because he'd be easier to beat, maybe that is true, but it might also be wishful thinking. The Dems might be believing their own and MSM-linked line that Trump is widely perceived as a hopeless idiot and buffoon, and that Hillary will mop the floor with him in the campaign. That doesn't mean it is true--we've seen how out of touch the establishment pols are in both parties.
Y’now, you present a ^delicious^ scenario.
Cruz becomes the R-nominee and is hamstrung by a court-action to determine his eligibility.
Hillary is the D-nominee and is hamstrung by a DOJ/FBI investigation (which would translate to her eligibility).
To paraphrase Fred Rogers, “can you say constitutional conundrum”?