The Genealogical database at the University of Montreal (PRDH) has no listings for Pardee. Pardie is a standardized name that includes Pardis and there are 5 listings from 1770 to 1850. As Rob indicated, it is probably derived from Paradis, which was used as a 'dit' name, so Paradis may have originated as Aubin, DesRoches, DeVidepoche, Dufresne, according to Tanguay's research from the 1870's.
The name Pardy is another possibility, but is an English name. There are 42 listings at PRDH from 1800-1850 and almost all are Presbyterian or Anglican.
If you have a first name and birthdate, it would be easier to narrow the search. Also, where they immigrated to in the US might help. Many times an immigration included other family and community members. The diocese of Montreal even set up Catholic parishes in the US and promoted the emigration within the diocese to the US.