No, you will need to go during office hours. They need to inspect your papers on the US side, verify the car's VIN number, and stamp the documents. Then you drive over to the Canadian side and show them the papers.
CBP will email you and tell you the operating hours.
Here's what my email said:
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Business hours are Monday through Friday from 8:00 a.m. to 4:00 p.m. We are closed on all U.S. Federal holidays.
Please arrive by 3:45 pm to allow adequate time to process your paperwork as our office closes right at 4:00pm or you will be asked to come back the following business day.
We are located in the Lewiston Bridge Cargo Warehouse- Room # 135
1 Lewiston Bridge Plaza Lewiston, NY (follow the signs for Customs Export)
The Lewiston Bridge is the only place to export a vehicle in Western New York
If you receive a response from us – Please do not resubmit the same VIN/Serial number – as it will be kept on file for 6 months.
Vehicles for export may not be brought to Canada or be in Canada prior to being formally exported by U.S. Customs and Border Protection. Failure to comply with the requirements set forth in 19 CFR 192.2 may result in a penalty action.