From what I've seen (which is not much) some Ansett LAME's ended up as flight engineers, but that was a long time ago.
I guess it depends very very much on corporate culture.
I can think of some corporate cultures where the mere suggestion of you becoming a pilot from an I.T. or engineering background would be regarded as "sedition" and would put an immediate stop to any future promotion and perhaps grounds for retrenchment in the next round of cuts.
To put it another way, the meta message you are sending your employer is "I don't have any long term commitment to this job or department, the real career I'm after is being an airline pilot, and that's the only reason I'm hanging around here".
Now while I guess this is acceptable in flying schools, It certainly would have been heresy in the old Ansett culture, and I don't know if it would be acceptable in Qantas either.
In fact, the only airline I can think of where this would be regarded favourably is Southwest (I think) in the U.S. of A. I have never seen a more motivated and positive group of people, one minute they are issuing your boarding card then its "pardon me" and they are martialling the aircraft and loading it. If you want to see "commitment" then seeing a girl wrassling with an external power lead that weighs more than she does, is it.