No, they don't. There is a proper industry definition of what a "mobile" number is and only "mobile" numbers can accept SMS from shortcodes.

All of the 2FA from FANGs and banks and so on come from shortcodes so you can't do a lot of those 2FA workflows with a twilio number (or a number you port to twilio).

As per engineers at the Signal conference, there are no plans to make proper "mobile" numbers available at twilio.