Can I install a replacement faucet directly onto a laminate countertop?
Sure you can.  I'd recommend using a sharp Forsner type drill bit or sharp hole saw to avoid chipping the laminate. Cover the laminate with painter's tape and mark your hole centers.  If your using a single 4" faucet fixture, use a template to drill the holes. If you are using separate handles/neck. the common spacing is 8 inches, but again, use the template.