My stock reply re: mechs in the Traveller Universe-
There are such units serving the Imperium or Regional armed forces in some capacity (one of the MT books) and designs and support for designs in various Traveller design systems. Treat mecha as another tool, another vehicle, another option not the only weapon needed and never forget to use combined arms and good strategy and tactics.
Most plausible for military/merc/spec ops/police types are "big BD" types like Shirow's landmates or hard suits, powered armor/BD like Starship Troopers (the inspiration for Gundam) Bubblegun Crisis and the like, and insect types like Shirow's Fuchikomas/Tachikomas*. Less plausible, due to being taller, Votoms, Heavy Gears, or more recently Gasaraki's units. A variety of drive modes would be helpful, and several of those units have such, usually a roller (wheeled) or tread mode. There's some possibilty for space use, esp. for modified forms like spheres or smallcraft/fighters with arm units.
Exoskeletons, like Aliens' walker, or bigger industrial/construction units, like Patlabor's labors are ok by me, and IIRC are depicted in T4. While they are getting too big really, the various tanks with legs by Shirow or in (esp.) Patlabor have some potential, and don't have to be much taller than a tank. Besides, the sight of a big spider crawling at undisciplined lower TL infantry is fun. ^__^
Given that Traveller is set in the Far Future, advancements in materials, construction methods, targetting, ECM, weapons, etc. give enough leeway IMO for a creative player or referee. Even Gundam has a scientific handwave of particles that screw up sensors and communication to very close ranges. That and people tend to view grav vehicles as very reliable and sturdy, when they could easily be vulnerable to a solid hit on a thruster or grav unit esp in civilian models or lower tech levels. For that matter there's nothing saying mechs can't have grav, as BD already can.
The main thing though is to have fun and not be limited to what any design system or rules state if it gets in the way. Mechs can be quite fun and allow for a mech for each character or a tank-like team mech.
* which double as robot units with base AI as well as carrying/driven by riders