I'm avoiding the Oscars tonight in favor of catching Metro City Boys live, posting to this blog and to Empire (see the Blog Roll), and doing some more work on this Sword & Planet story I've been tinkering with lately.
While doing that tinkering, I came upon some additional 80s anime that you folks coming over from the Castalia House blog ought to checkout. To my knowledge, they didn't influence the early FASA BattleTech, but considering that similar elements exist and you can make an argument for a six-degrees-of-Kevin-Bacon level of influence.
The big change to BattleTech came with the 3050 Technical Manual and the Clan Invasion of the Inner Sphere. In addition to the far superior BattleMech technology that the Clans wielded, this was where the game introduced Battle Armor in the rules and the setting got heavy on the eugenics and messed about with genetic engineering. The latter two elements are key in a 1983 Japanese TV series by the name of Armored Trooper VOTOMS, where the mechs are powered armor and not giant stompy robots and the pilots are enhanced humans. (Now you see what I mean by that roundabout influence.)
This series has that '80s malaise I spoke of previously, so expect a certain degree of cynicism and bleakness. This is so for the series, the comics, and the OVAs made thereafter. While the specifics behind the enhancements that the soldiers get vary widely between this series and BattleTech, you will find it in the latter- especially later on in the latter's timeline when the Battle Armor technology gets into Inner Sphere hands, and news of Jade Falcon's sub-dermal enhancements on top of eugenic and genetic programs gets to Inner Sphere leaders.
In short, VOTOMS is a pre-existing series that shows you something that should exist--and, eventually, does--exist in an environment such as that positing by FASA's BattleTech. These powered armor aren't the sleet Iron Man armors, but instead car-sized units like the smaller Autobots of Transformers fame. (As the Infogalactic article shows, this series not only got a licensed tabletop RPG from the makers of Mekton Zeta, but greatly influenced Dream Pod 9's Heavy Gear; having played the later a lot, the influence is very strong indeed.)
Unlike the posts I made on the anime origins, I put this up for you--the player--in considering how to approach things many put outside the core experience of BattleTech, to include or not at your discretion. (Me? Not that keen on it myself, but I do get why others like things such as the armors. I prefer to stick close to the core experience of Big Men using Big Machines to get Big Things done.) This is all For Your Consideration, and it bothers me not at all if you decline to use it for your fun.
As for the series itself, it did get a commercial release, but ease of acquisition varies. Of course the fan-run resources can and will deliver, if you look long and hard enough. Below, subtitled, is the Shining Heresy OVA from 1994. You can search for the rest yourselves.