I can't speak for everyone as I'm sure there are some out there that would say you can do it. I'm equally sure you'll get plenty of people [sarcasm mode] incredulous that you could ever be stupid enough to do an integrated course.[/sarcasm mode]
However, to answer the questions asked, in my experience: forget it. There is no chance you could work part time and do yourself justice on the course. Lessons are 8:40- 4:30 ish and you WILL need to do about three hours per night on top of this to stay on top of it. You could choose to work weekends etc, but I would suggest you'll find yourself so knackered out that you'll desperately need this little spare time to cling to any shred of life outside of ground school. You will also probably need to factor time at the weekends as well.
Beware that there will instantly be replies saying something along the lines of "Pah, I don't know where monkey nuts here has got this from, you can do the whole lot in three months on two hours a night". It may be possible to do this and pass the exams - I just don't know, but I DO know that half the point of an integrated course is to ensure you know the material inside out. Again, I can't say that those that "did it in three months" don't know the stuff, only state the belief that from my experience, unless they're ex-military converting to civvy, they almost certainly won't.
Do NOT underestimate how hard the path is...it was a real eye opener for me and just about everyone I know that has/is treading it...
good luck