So I've been playing around in the US Census OnTheMap tool, looking at work locations for residents of different areas. What I've found so far suggests that there likely is demand in southern New Hampshire for commuter rail to Boston.
First, I drew a polygon rougly surrounding the rail corridor by 3 miles on each side, which was enough to encompasss almost all of Nashua, all of Manchester, but excluded Londonderry and Derry. This area counted about 150,000 workers, of whom 30K worked in Manchester, 23K worked in Nashua, just under 5K in Concord, and 3.5K in Boston. (I can provide the OTM settings files for these, if anyone is curious.)
On the face of it, this might seem like a rather low share of commuters to Boston. (Although also worth noting that Lowell itself has similar numbers, suggesting that it might be a destination unto itself.)
However, I then ran a similar analysis on Providence + Pawtucket -- roughly 3 miles on each side of Providence station and South Attleboro (slightly larger to account for better bus coverage). This yielded a similar number of workers: 142,000. Of those. 40K worked in Providence, 10K in Pawtucket, and cumulatively 25K worked in Cranston, Warwick and East Providence.
But -- and this is the key point -- Boston itself came in with almost exactly the same number of workers as it did on the NH analysis: 3,800.
So... at a similar distance, there are roughly as many PVD-BOS commuters as there are NH-BOS commuters.
And there's a stronger "halfway commute" market with NH-Lowell, and that's
with having to drive at least halfway.
And just to sanity check myself, I ran a similar analysis on Fitchburg/Wachusett/Leominster:
A larger, though similar, share of commuters to Boston, and a lower number overall.
The numbers suggest at least some superficial similarities between Providence and Nashua/Manchester, as well as a pretty clear exceeding of the lower bar set by Fitchburg. Commuter rail to Boston "works" from both Providence and Fitchburg, suggesting it could also "work" from New Hampshire.
I know it's not a perfect comparison, but it does seem worth considering.