I see some niche uses for an Artillery 'Mech, and could probably justify having a lance of them in a battalion-sized formation, but the primary artillery compliment of the unit is still going to be either vehicle-based or towed.
As pointed out previously, it doesn't take much effort to put a Thumper piece on a turret-less Vedette, particularly if you're willing to live with a slight drop in speed to 4/6. There's enough mass free to put in the artillery piece, 2-3 tons of ammo, and a small backup weapon (SRM or MG), and still armor it well enough to handle near misses from counter-battery fire. A Sniper gun can be mounted instead, but there are some serious design trade-offs that need to be made, and it will likely need some kind of bodyguard unit for protection.
Assuming 3 turns of flight time after firing, that's enough to get up to 12 hexes away from your last position before your shells land, and the enemy won't even be able to get a fix on that last firing position until the last turn or two before impact at the earliest. They then have to fire their own guns from BEHIND their lines, which means 3-5 turns before that fire arrives, by which time you could be as much as 21-32 movement points gone from there and ready to either fire again, or counter their counter-battery fire as soon as it's triangulate. Firing from further away leads to lower accuracy and a greater delay between spotting and arrival, but makes it virtually impossible for the enemy to effectively use counter-battery fire against you.
Except for the tactical use of Arrow IV homing rounds, where a 'Mech makes sense as a firing platform, I don't see too many cases where 'Mech-based artillery has an advantage over a Self-Propelled Gun. At the strategic level, the vehicle can do the mobile artillery job for a lot less cost, and where the mobility isn't required, towed guns are the obvious answer.
