I have a similar setup with a backup gennie at my place and only once I have had the furnace act weird, and that was when the gennie was loaded down and the voltage dropped to around 100 or so volts... The furnace control board kept picking up and dropping out the fan motor but that was about it.... I did have to tweak the govenor on the gennie to make it produce the proper output at the proper frequency under mid to heavy load and since then I have had no problems whatsoever...
Believe it or not, with a 4500W gennie I can run 2 referigerators, a freezer, and THEN start up my furnace and Central A/C and have no problems..
A.D
