No. Chrome was so much better than Firefox it wasn't even a contest. Firefox, when it came out, was honestly pretty crap - I tried it and went back to IE in pretty short order because it was noticeably faster. Chrome was a huge leap over either IE or Firefox when it came out, and people switched for that reason.

That is a weird alternative history. Even by Firefox 1.0, it was a dramatically better browser than MSIE in every conceivable metric -- except for support for Microsoft's proprietary extensions like VBScript, ActiveX, and NTLM auth support. (It also failed to replicate some of MSIE's most outrageously terrible bugs.)

When Chrome was released, Firefox was four years old and had already gained 33% market share with momentum on its side, mostly through word of mouth. Chrome was a bit better in some respects, a bit worse in others, but it had the Google marketing juggernaut allowing its market share to skyrocket.