You won't have any issues. You don't even need to have proof that the application is paid or in progress. I cross the NY-QC border every weekend and they have never asked me for proof and never had an issue.
Now it's better if you get a beautiful visitor record. I didn't ask for one, heck I didn't even know those beautiful records existed! until one day an officer gave me one and told me I could stay until I get PR status.
Don't be nervous.
