GMAT is definitely a factor in deciding who makes the MBB closed list, however its importance varies by firm. At BCG for example, it is a relatively minor part of the resume screening criteria (less important than the prestige of your schools and employers, your professional experience, and your leadership and communication skills). In terms of the actual score, anything below 680 is a detractor, 750 and above is a positive, and 680-740 is considered neutral.
McKinsey has a greater emphasis on high (700+) GMAT scores as well as their problem solving test (PST)
My general advice to candidates is that if you have a 700+, you have basically checked the box for the "raw horsepower" the firms are looking for and should be focusing on presenting your background well on your resume, networking effectively, and then getting ready for those (hopefully) upcoming interviews.
-Jeff