I worked for a relatively high profile NYC restaurant during college which had a relationship with AMEX. Every night, two tables would be automatically "blocked" for AMEX at primetime (it was programmed into OpenTable). If an AMEX concierge called and the tables were available, they were given to the cardholder. However, sometimes our manager would tell us to delete the AMEX blocks mid-afternoon so it really depends on the restaurant. When I worked the phone, I'd always try and help out AMEX because they issued me my first CC as a student with zero income and I liked the company.

Restaurants with a formal agreement with AMEX, which follow that agreement, are going to work pretty well. Restaurants without such an agreement are YMMV all the way.