Okay, if you're talking about an one-off thing the mega-wealthy came up wtih, sure. But it's not going to be a widespread thing. You might have some sort of leisure planet with that sort of stuff but I don't know of any that was actually
written into the setting. It would definitely not spread outside that one system and without backing of a large corporation or a House it's not going to become a House or Sphere-wide event because interstellar travel isn't exactly a casual thing in BattleTech.
And even then, non-combat 'Mechs are not actually the best at anything except going over rough terrain. Sure, you can have a stunt LAM, but it's still going to be worse than a stunt Aerospace Fighter in the air and a Locust on the ground. Anything that needs to go over rough terrain can usually be done by a tracked vehicle. A mobile nightclub might as well be done on the back of a stripped-down
Maxim II (it hovers so it's cooler). The quad ideas could work but again: you need custom-made designs or
very heavy modification of existing designs. You
could have that sort of stuff, but they'd universally be one-offs that just don't get written into the setting due to space.
Now, fair play: I'm pretty sure I saw something about an expedition or safari on the back of a quad 'mech in some book somewhere. But again, very one-off thing.
I'd say leisure Mech designs would be more than a one-off thing, but they would certainly be rare, yes! Except for maybe an APC/IFV Mech, and civilian variants of old/mothballed Mechs that've been tricked out as personal "garage projects" by Tech-minded 'warriors, there might not be a
huge demand for leisure Mech designs - but there would be some demand, of that I'm certain.
And sure, there are ways to fill many of those functions more cheaply using conventional vehicles, like having a nightclub hovertank instead of a nightclub quad, but the same can be said about ANY role Mech's play. Battletech is not exactly a "practical" setting; it's a setting where galactic armies have for centuries decided that giant stompy Mechs are preferable to cheap, reliable tanks in almost every role. If the galaxy's moneyed class are willing to build Mechs instead of tanks for the life-and-death rigours of combat, then I think they'd be willing to build Mechs instead of tanks for hauling nightclubs around.
(besides, imagine if it was you:
"Hey Cornflakes, would you like to come take a ride in a Mech?" OH YES PLEASE
"By the way, this Mech has a built-in swimming pool and Holovid lounge where former Solaris girls serve you the finest Skye whiskey" cooome ooonnnn, nobody would pass THAT up, right? It'd be like Space Disney. Practical or no, you'd make a killing with resort Mechs.)
Another thing I was thinking:
hunting Mechs. As in, Mechs designed, or modified, primarily for hunting alien species, ranging from small game to predatory megafauna.
These Mechs would have limited weaponry; one large bore weapons system (PPC), a couple point-defense weapons (flamer, SPL), and possibly a melee weapon for tackling megafauna up close. Engines would be enlarged, armor would be stripped to a minimum, and a "crew quarter" would be added so that a pilot and/or several passengers could live in the field for several weeks or months if need be (this crew quarter could include an observation deck from which operators can fire conventional weapons, like sniper rifles and hunting lasers). Maybe there'd even be a refrigerated storage box where alien animal parts could be stashed?
Mechwarriors are basically medieval knights, and the one thing knights enjoyed more than jousting (Solaris) and maidens (Canopus, Elementals) was hunting. So I'm sure sport hunting is something that nobles would do, especially on planets with lots of nasty fauna. And from what I understand, there's a number of planets with really nasty aliens living on them, including a few that are so bad they've wiped out entire colonies before. So on some planets it wouldn't just be sport, it'd be practical culling.
Perhaps there's a planet full of big, dumb Kaiju, stompy beasts who are the size of Battlemechs? This world is remote and far from the warfront, so bored nobles living in the area like to come and try their luck fighting vicious Kaiju. Many hunters blow their targets away from a distance, but a number of madlads feel this isn't sporting enough; instead, they like to close with the Kaiju for bare-knuckle brawling matches, or else use bizarre, custom-built, "low tech" weapons systems - like a
Mech Spear designed for stabbing at a distance, or a
Mech Bow, with myomer bowstrings, that can launch ferro-steel arrows tipped with a single SRM.
Or, maybe Dumfries IX, an agroworld of largely Scottish ancestry known for producing the sector's most robust herds of spacesheep, has become overrun by genetically-engineered Kangaroo Griffoxes? These vile predators swarm in packs and completely overwhelm the planet's conventional forces, swooping in and destroying entire garrisons with a combination of vicious kicks and spammed MLP pornography. Rather than lose precious farming colonies, the local rulers have decided to call in Hunting Mechs to deal with the marsupial menace.