Las,
Correct a Mitzvah is enough for Techumn, same reason you can use it for a Chasunah etc.
And that is exactly my point regarding the Maharil forbidding an Eruv for Minyan – that its basically only a “hidur” in Mitzvah of Tefilah not a complete mitzvah, at least shitah of the Mahril, the M”A disagrees though .
And I think the Tosfos R”P in Eruvin also paskens like the Maharil.