Can glaucoma be picked up in eye test?

Yes. Glaucoma screenings can involve checking vision, eye pressure, peripheral fields, and optic nerve appearance. However it usually takes more than one exam to definitively determine glaucoma (progressive nature) unless it's obvious end stage.
No. If you are using the term "eye test" to mean a test of your vision only, as you would have at the motor vehicle office or at school by a nurse, the answer is no.
Yes. Pressure check and dilated exam. If the damage is very severe, it can sometime be detected incidentally by the patient or with confrontational visual fields (finger counting tests in side vision).