I am hoping to complete two years at CC before transferring and completing my degree. Would a prolonged stay at a CC greatly affect my admission chances to engineering programs?
No. why do you think it would? All you need is the GPA, the pre reqs, and no failures in any major prep classes.
Some schools will only accept transfer students who have completed two years (and taken all of the critical tracking course). It really shouldn’t hurt your chances.
Look for a CC that has a transfer program with a close by engineering school. I know in NY they have some. It will make the transition easier.