Can I have regular teeth cleaning while also having Invisalign treatment?

That is one of the beautiful things about "removable" braces is that it facilitates keeping your teeth cleaner. Thus there are no metal brackets or bands to collect / trap bacteria and debris. I would actually suggest that you get 3 cleanings per year while doing Invisalign treatment.

The foundation of a healthy mouth is to have a dental cleaning at minimum TWO times a year. During orthodontic treatment some patients require to be seen more often. Check with your treating dentist.

When a patient is wearing traditional metal braces, one of the biggest challenges is keeping their teeth clean. The brackets would trap food and debris. The aligners from Invisalign come off any time a person wants, so eating and brushing is a "non event". The same applies for trips to the dentist, as the aligners can be removed for the entire appointment.