No.
Shipping rates are only calculated and displayed during checkout. Shopify does not provide real-time updates inside the cart page, so HideShip rules apply only at the shipping step.

Also, Hideship works on the exact name of the Shipping method and can read the change of the method name.

Best suggestion if you have a list of dynamic rates with the same name, you can use this way to identify and sort or hide:
*name of the method in common*

Example:
If you have multiple dynamic shipping methods like:

UPS Standard shipping 2-3 days
UPS Internation Shipping 4-6 days
UPS Express 48h

You target all of them like in the screenshot

This method will allow you to hide or sort all those methods at the same time