No, generally speaking your website should not go offline on Black Friday. If you are using shared web hosting and your next door neighbors are ecommerce sites. The ecommerce sites may get a surge in Internet traffic. That traffic should not result in your website going down. The web server that hosts your website may experience some slowness.
Your web host will have policies in place to deal with a surge in traffic to a certain customers website. No web host wants one customers site popularity to knock all their other customers offline. Any surge in traffic on Black Friday should not result in your website going offline or having an outage.
If you notice any slowness or your website performance is not as usual. You should open a trouble ticket and let your web host know so they can investigate and make sure they identify the possible causes of the issue.