This is going to be a somewhat deep cut, but on pg 8 of Schmidt's Petraries, the Seeker Keshik of The Scorpion Empire's Seeker Galaxy has modified their Star Leauge era mechs to carry Elementals. The Keshik is an Elite Supernova, and 3 mechs out of each Star have to be Star Leauge Mechs. So it's possible for standard Mechs to carry Elementals if they've been modified before hand. I'm assuming that second line/solahma units would either use vehicles like the Svantovit, Badger C, etc to move Elementals, but I can't think in the almost 300 years since Elementals were put in place some other enterprising Clan tech or commander didn't think of modifying standard Mechs to carry them.