I am updating my wet bar area with a new sink and faucet. Can I install the new faucet directly onto the laminate countertop so that I can use a separate no-hole sink?
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.
Yes, you can install the faucet directly into the laminate countertop. I wouldn't use an under-mount sink with a laminate countertop, because the corners in a laminate countertop are weak points. But a separate faucet with a self-rimming sink should be fine.