Will my abs light come on if my brake pump is going out?

My 1995 ford ranger's abs light is off once I start my truck and the turns on after I roll about 20ft. And in the time before that 20ft when the light is off, if I press the brake too hard the brakes lock up. Once the light comes on braking for is basically normal

Brake pump… You made that up. Maybe you mean power brake booster. The ABS light will come on when there are problems with the ABS. The power brake booster is not the ABS. See if your brake fluid is low.