I believe you may be talking about a TN visa, which allows a national of a NAFTA country to gain employment in another.
Quoting CIC on this:
While U.S. citizens seeking a work permit as a NAFTA professional,
intra-company transferee or a trader/investor, are eligible to apply
for a work permit at the border, they can obtain advance determination
by applying to CIC. For business visitors, NEXUS represents a
mechanism by which they can obtain advance adjudication.
As with any border admission, the decision lies with the agent. They most probably have access to CIC info in order to grant you TN status. According to CIC you are allowed to have multiple ongoing applications, and you can choose to withdraw one
Procedures for the processing of multiple general applications
There are times when clients decide to file a second application when they
already have an active application for the same case type. [...] In
general, the CPC-S accepts the second application and enters a bring
forward (BF) date until the outcome of the first application is known.
The second application will remain on hold pending the outcome of the
first application. The CPC-S usually contacts the holder of the
initial file to determine what action should be taken depending on the
circumstances of the case.
If the client chooses to withdraw the first application,
the CPC-S will send a withdrawal form to the client. Once the signed
withdrawal form is received, the CPC-S will inform the local office.
The local office will return the first file to the CPC-S who will
close off the file and proceed with any refunds. The CPC-S will enter
the second application into the system and send it to the local office
for processing. If the client chooses to withdraw the second
application, the CPC-S will send a withdrawal form to the client. The
CPC-S will close off the file and proceed with any refunds once the
signed withdrawal form is received. If the application is withdrawn
before the “capture” stage is completed, the total fee is returned. If
the application is closed off after the “capture” stage is completed,
then only the Right of Citizenship fee is refunded.