No. Shops are required to run OBD diagnostics on your car if it’s under 20 years old by law, there isn’t leeway given if it fails emissions tests.

However, if you’re in a bind and don’t have the money to fix it right away, if it fails, ask the shop for a clear sticker. Some may offer it to you, some may fail you and not mention it, but a clear sticker will give you the option to have it temporarily inspected for 90 days while you get the emissions issue fixed. This is only for emissions problem though, if it fails for safety, they won’t give you one until the issue is fixed.