Can Heimerdinger use the tap ability of Renata to gain a point even when not on a battlefield?

Yes. Heimerdinger can use Renata's exhaust ability from base to gain a point.

Heimerdinger copies Renata's exhaust ability (pay 4 blue, tap 4, and tap himself → Score 1 point) but does not inherit her passive battlefield restriction. That restriction is a separate line of text, not part of the exhaust ability itself (Ref: FAQ 650).

One caveat: Heimerdinger still needs 4 blue runes, 4 channeled power, and the ability to exhaust himself. And since he can only exhaust once per turn, you can only fire this ability once unless you have a way to read