Well, the EHA does rely on 02 sensor input, but only after the engine warms a bit, and the 02 becomes active and goes into closed loop. Upon cranking and initial warm up, the EHA is programmed with a set value depending on temperature. During cold cranking, the EHA sets at +20Ma, very rich. Then when the engine fires, the current drops according to the engine temp, usually about 4-8Ma. When the 02 goes closed loop, the EHA will modulate, optimally around +-1Ma. So, yes the EHA could cause lean running during warm up if it were faulty and not responding properly to the requested current.
But, if it were faulty, it would probably also indicate a warm-engine adjustment quite a bit from the nominal 0 Ma or 50% duty cycle, as it tried to follow the 02 sensor inputs.
But, as mentioned in the earlier posts, a lot of other things could cause poor cold-engine performance; the #1 culprit probably being injectors.

EHA's seem to be pretty robust, the biggest fault being fuel leakage, which is very obvious. First test might be to check warm duty cycle on the diagnostic connector and see if it's in spec at about 50% +- 10, at both idle and 2000 RPM (do a search for the procedure). If it is, then the EHA is probably OK, as well as the air valve setting. If it's not, then the search begins; vacuum readings, air valve adjustment, fuel pressure, then actual EHA current monitoring.

DG