There's a 99% chance that they have a build process in place already, if for nothing besides minimizing and concatenating their JS files. Adding the `tsc` step is pretty minimal overhead, and all valid JS is also TS; although the language service is going to complain about the lack of types, everything will still work exactly as before.
My argument is that in general, it will cost more in time and effort to add types to a more mature product than to keep them up-to-date in a young product. It's like good comments and documentation - either go 100% or accept that you're going to have a lot of tribal knowledge that is difficult to efficiently disseminate to new employees.
Putting pain off until tomorrow is perhaps good for business, but not for people. Remember that developers are people.