Don't think they should (or will) use it.
That said, if they like someone who's otherwise a minimum salary player, and/or someone from Europe, I would be okay with using a portion of it on such a player.
Say, for instance, Danny was comfortable enough to offer Oden a deal (Hypothetically people, I don't want to start a debate about Oden!) He's looking at getting the minimum, which is around $1 mil for someone with his experience. If Danny gave him $1.25 mil to get him to come here instead of say, Miami, I'd be down with that (again, assuming that he has reason to believe Oden can still walk.) Or say Gigi Datome was looking at a minimum salary offer from Memphis. If an extra $100-$200k in that first year gets him to come to Boston, that seems like a good use of the MLE. But he shouldn't splurge on a single player to add to this roster.