Yes. In your case, it would likely be easier to walk than take the shuttle since Terminals (7/8), United, are directly on the other side of the parking garages that seperate the two terminals. Right now there is a lot of construction going on at the Tom Bradley International Terminal (both outside and inside...and traffic lanes are blocked) and that can hold the shuttles up.

Best if you walk out of the Terminal 1 secured area onto the departure/check-in area of T1 rather than going downstairs to the baggage claim area (this way you don't have to cross road traffic). There's an elevator just outside the building where the Southwest check-in area is that will take you to an elevated walkway that crosses to the parking garage for T1. The T1 parking garage is connected to the T7 parking garage and there is another elevated walkway from the T7 parking garage that takes you to an elevator that takes you down to the Terminal 7.

Waiting for the elevators might take up most of the time...I'd say 15 minutes at most to get from one to the other.

Alternatively, if you want to avoid the elevators, go to the ground level (arrival level) and cross the street, walk into the garage and keep going until you are on the other side of the T1 and T7 garages, cross the walkway to the arrival level of both T7 and T8 (which are connected). Take the escalator on the outside of the T7/T8 area up to the United check-in area.

Here's an illustration of the what I've posted. http://www.airport-la.com/info/terminal_map.html