They could do, as long as they have some kind of a work permit/status, such as
TN (for any job titles as specified by NAFTA) or L-visa (for transfer employees, employed with the company for at least one year)
No Canadian citizen may work in the USA unless he/she is legally allowed to do so. Just as no US citizen may work in Canada without without being legally allowed
If you're asking for yourself, and would work at the US branch as a consultant, then you're in luck because consultants qualify for TN status. However, it is also a highly scrutinized title due to abuse and misrepresentation. If you're really a consultant with the proper background and can prove it, then it shouldn't be a problem at all. TN's are easy enough to obtain at any port of entry. The TN letter would have to be written by the US branch though. Not your Canadian office. That is my understanding anyway.
Try and do a search for consultant on this board, I'm sure a lot of information will pop up.
Hope this helps!