AFAIK, DMUs will not be allowed through the link. Only electrics, EMUs or dual-mode locomotives will be able to enter the Link.
That's really the big expense. Buying new fleets of vehicles and electrifying lines that will be using the link. NEC is already electrified, but there's no capacity for any 'MU frequency routes along the NEC.
The issue from through-running as I see it, is that every northern line (Fitchburg, Lowell, Haverhill, and Newburyport/Rockport) has both the capacity and the demand for some sort of inner 'MU-type service. Of the southern routes, only Framingham/Worcester and Fairmount have the capacity and the demand to implement 15-18 minute headways.
Worcester can handle it with signal and passing track upgrades. Fairmount is already ready for RT-like service.
Old Colony can't handle high headways due to the pinch in Dorchester. Removing that pinch is a megaproject all its own. Old Colony probably won't get a portal into the Link until that's done. It's fiscally a dead end.
The NEC will be handling both higher frequencies of Amtrak service as well as higher MBCR traffic - especially after the Link is built. Projected congestion on the NEC will already eventually box out the Needham Line by choking it to death, so there won't be any capacity on the NEC for an 'MU line to Needham. Needham's getting choked to death by the NEC's growth and will eventually need to be replaced with a Green/Orange paired extension. That means there won't be any 'MUs running 18 minute headways on the NEC. The capacity isn't there now and won't be there in the future.
If routed along the Fairmount, the Franklin Line could probably handle high headway service to Norwood or Walpole.
The first southern Link portal to be built will be for the NEC, which will likely also include access for the Worcester Line (which would need at least partial electrification). The northern portal will likely be able to include both the Lowell Line and the Eastern and Western Routes (electrified). Fitchburg will probably never get one. Problem is, the Worcester Line will only be able to handle one high headway 'MU line (pick a through-run option to Lowell, Reading or Salem/Peabody).
With the initial build there's no other option for routing 18 min headway 'MUs through the link. That leaves any 'MUs running on the remaining four northern lines to terminate on the surface at North Station.
The next priority should probably be electrification and portal construction for Fairmount and maybe some of Franklin. There won't be as much demand for an RER to the Fairmount since there's no employment centers along it. Commuters will take a Link-running train to South Station, but not many will stay on beyond that because the Fairmount runs through residential neighborhoods. That lack of demand, and the high costs of building the portal and electrifying the line will make this one a political battle, but it's still probably the easiest way to get another high-headway line through the link.
Old Colony will have to wait until the Dorchester mess is funded and fixed, and Needham is getting squeezed on its existing schedule, let alone at higher headways.
Realistically, as far as transformational 'MU-type service goes, the most to expect is two high-headway,through-running routes (something like Lowell - Riverside and Peabody - Walpole). That's it.
EDIT:
Here's something like what I'd envision for post-Link 'MU service, once two southern portals are built:
Indigo Lines Map
There would be two through routing lines From the South side. One from Riverside or Framingham, and one from Dedham or Norwood. On the north side, only two lines would receive those trains (if high headways are to be maintained). Pick two from Peabody, Reading, or Lowell. The Fitchburg line's 'MUs will always terminate on the surface at North Station.
