Can Heimerdinger empower himself if there's a Hextech Disc on the board, or not because of how empowering is ruled in general?

Yes, Heimerdinger can empower himself using Hextech Disc's Empower ability.

Heimerdinger gains every exhaust ability from friendly gear — including Hextech Disc's Empower [T] ability. When he copies it, "this" in "Empower this" refers to him (the new source of the ability), just like how he copies Renata's exhaust ability without inheriting her passive restrictions (FAQ #9851). So he pays [T] (exhausts himself) and becomes empowered.

A couple of caveats:

• He can only activate Empower if he isn't already empowered (Rule 827 — "Use only if not Empowered").
• He also gains Hextech Disc's other exhaust ability (Disempower this, [1], [T]: make a Mech token). Since he can only use one exhaust ability per exhaustion (FAQ #8927), you'd need to choose which one to activate each time.