While I have heimerdinger, Academy Instructor on a battlefield and I activate Vanguard Armory. Does this count as playing a token, and instead play 3 mech units.

Yes — Vanguard Armory's three Recruit tokens are three separate "play a token unit" events, and Heimerdinger's replacement effect has no once-per-turn limit, so each one can be swapped for a 3 Might Mech token instead.

You choose per token (it says "you may"), and each Mech goes to the same location that Recruit would have gone to — so you can still spread them across your Base and any battlefield you control. Because the Mechs are actually played, they still count as playing a unit for triggers like Legion.

One condition: Heimerdinger must be at a battlefield himself, not at your Base — if he's sitting at Base, the ability doesn't apply and you get the three Recruits. (Rule 371.2.a — replacement effects are applied per event, and the player controlling them chooses each time.)