enabling offline mode in your app has nothing to do with your online store. you can take payments in offline mode (though I highly recommend you find a way to have internet either via tethering or local WiFi to mitigate any payment failures with the much higher risk of offline mode.) Your store is running on servers unrelated to your app.
Offline Mode doesn't impact your Online Store as @VanKalkerFarms mentioned (thanks for chiming in 👍🏼 )
You might want to check out this existing article that gives more details on how to best utilize Offline Mode and how to protect yourself with these types of payments if you don't have internet access at your craft show:
