...like maybe the electronic cigarette will interfere with the process.
I really don't believe this will be the case. You've got to remember that there are TONS of ugly chemicals in cigarette smoke. Some cause cancer. Some contribute to (but don't necessarily cause) heart disease. Many of the others have a mechanical effect on your lungs. i.e. - they gum up the tiny hair like structures already mentioned.
e-cigs, while probably not "good for you," have a VERY short list of chemicals in them. There's the nicotine (contributes to several types of heart disease but is "probably" no worse than drinking too much coffee), the PG, which is pretty dang safe, and the flavourings.
I have no idea how safe/unsafe the flavourings are long term, except that they are almost certainly FAR safer than smoke.
The think that causes you to hack up all that lung-butter when you quit, is the tar. A mix of smoke and moisture that leave deposits in your lungs that are pretty similar to what coats the inside of a chimney. There's not tar in an e-cig.
It's just an educated guess, based on my limited experience, but the e-cig may HELP you cough it up. I switched from analogs (American Spirit) to a blu back in July. Like all smokers, it wasn't the first time I had 'quit.' I found that I started hacking up stuff the next day. This could be easily explained by the fact that the vapour is mostly water, and that water may have a "rinsing" effect. Granted, I don't even vaguely resemble and expert and my experience is limited, but that's my best guess.