Straight EMU's these days all have small batteries for preventing 'gapping' under short dead sections, so there'd be no need for BEMU's and true discontinuous electrification.
The bigger issue here is the service levels. Does Providence-Woonsocket really merit better than hourly service? The densest areas are on the NEC where overlapping Providence Line and Providence-Westerly service keeps the headways stiff. The P&W is much sparser, and only hosts 2 small and widely spaced intermediate stations. If you can't justify better than hourly, it's going to be tough to pay back the electrification investment and you're probably better off just leaving it diesel.
I'm glad you raised that point, because that's kind of where I was headed. I think the overlap could impact the calculus on whether to electrify north of Boston Switch. Hopefully this will make more sense if I frame it in terms of why you'd be looking to run service to Woonsocket in the first place.
If your goal is simply to offer rail service to people in the Blackstone Valley, then yes, a conventional Woonsocket-Providence service could get by with hourly headways and diesel power, especially if stop spacing is kept as wide as the
Providence Foundation study proposed (just three intermediates at Manville, Cumberland, and Pawtucket). But what if you view running service to Woonsocket as incidental to the goal of doubling frequencies in the Providence metro?
Say you’re already running a Westerly-Pawtucket service with EMUs, and your main priority is to add another service layer that has both layers overlapping between Warwick and Pawtucket. This cuts headways in half, so you now have trains going through every 30 mins, or maybe even 15 mins. You want to take advantage of the frequencies by adding dense infill stops in that overlap area, and for performance as well as uniformity of fleet/maintenance considerations, EMUs are the rolling stock for the job.
Although most of the ridership and demand is going to come from the segment between Warwick and Pawtucket, you recognize this second service layer could also serve the Blackstone Valley if you extend northwards beyond Pawtucket up to Woonsocket — but electrification currently ends at Boston Switch.
If you don’t want to take on BEMUs for maintenance or performance reasons, could there be a world in which the lower-frequency, wider-stop-spacing, Pawtucket-Woonsocket segment of the overall Woonsocket-Warwick corridor gets catenary not because it warrants it on its own, but because the higher-frequency, denser-stop-spacing, Pawtucket-Warwick segment needs it?