Invisalign and other clear aligners (also called invisible braces) can involve anywhere from six months to two years of use. They're typically faster than traditional braces, but you're still going to be wearing them for a reasonable period of time. So what happens if you need a root canal during this time?
Root Canal Treatment
A root canal is needed when the tooth's pulp (which is its nerve) has become inflamed and infected to the point that recovery is no longer possible. The tooth is opened so that the pulp can be extracted. The empty pulp chamber is then thoroughly irrigated before being filled with a latex material. The tooth is then sealed with a filling. Wouldn't it be wiser to wait until after your orthodontic treatment has finished?
Waiting isn't an option, or at least, not an option you want. One of the hallmarks of an inflamed dental pulp is pain, which will only become worse without treatment. Since your aligner trays can be removed as needed (and you should only be removing them to eat and brush your teeth), it's not as though your dentist will have any trouble accessing the tooth in question.
In the days after root canal treatment, your tooth is likely to be sensitive. Clear aligners apply light pressure to teeth, encouraging them to move as the bone holding them in place remodels itself to support this repositioning as it happens. This process may be unpleasant if your aligner trays are used immediately after a root canal.
A Brief Delay
Your dentist (in consultation with your orthodontist) may recommend that you wait before you begin to wear your clear aligners again. This is only to spare you from the possibility of heightened sensitivity and is just a temporary measure. You won't have much time off, and it will only be a matter of days before you can wear your trays again.
A Short Extension
Because it was necessary to interrupt your orthodontic treatment to receive your root canal, your time wearing clear aligners may need to be extended. This isn't exactly a major disruption, and it might be that your orthodontic treatment will be extended by a week—which isn't a massive annoyance.
Not only can you get a root canal during orthodontic treatment—you should. It may not be convenient to need a root canal while you're in the middle of your series of clear aligners, but an inflamed dental pulp must be dealt with as soon as it's identified.