The sentence is correct and usable in written English. You can use it to describe a situation when people are allowed to register for something on a first-come-first-served basis. For example: "Registration for the conference is on a first-come-first-served basis, so make sure to register as soon as possible to secure your spot!".
Eligibility was on a first-come-first served basis.
Tickets are available on a first-come-first served basis.
And those would be on a first come, first served basis.
There will be limited spots available, so access is on a first-come, first-serve basis.
Entrance will be on a first come, first serve basis so REGISTER NOW! Video: Unitaur Attacks!
Entrance into the field is on a first-come-first-served basis with online registration starting next Wednesday.
Seats will be on a first-come, first-serve basis.
Awesome tool! I started using it one year ago and I never had to look for another app
Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia