I never got notice of this follow-up. Actually it is a new subject matter unrelated to the H1B question and should be a new question thread.
As a courtesy, yes, there is a problem with that.
When they come through customs they will be flagged as an intending immigrant living here.
Canada and US have a cooperative information sharing agreement so the US knows they departed the US and re-entered.
Mexico is starting to implement the same system.
Section 214(b) is part of the Immigration and Nationality Act (INA). It
Every alien shall be presumed to be an immigrant until he establishes to
the satisfaction of the consular officer, or at the time of application for
admission, that he is entitled to a nonimmigrant status...
The burden is on the applicant for entry to prove they have maintained their residence abroad. Generally that means they can demonstrate
permanent employment, a domicile, meaningful business or financial connections, close family ties, or social or cultural associations, which will indicate a strong
inducement to return to the country of origin.