I would suspect the garage bypassed the ammeter, possibly due to the new alternator exceeding the ammeter range or maybe by accident if they didn't know what they were doing. Note that a fully charged battery will draw little or no current, but should show some short term charge current after start up, assuming it is still connected.
Either way the alternator could well be charging the battery fine as they have suggested. Quickest way to check is with a voltmeter directly across the battery terminals. It should read 12.7 volts for a fully charged battery when engine not running. After engine start with revs above idle, it should immediately rise above this eventually hitting 14.4 volts give or take.
Centre zero ammeters are very useful instruments but lost favour in the late 60's when the dynamo was replaced by the more powerful, efficient and compact alternator. As these ammeters recorded all current in and out of the battery (other than starter) their electrical location added unreliability and may have contributed to their demise, not to mention cost. A voltmeter is almost as useful, cheaper and much easier to fit.
I agree. On all 3 of My Morgans I have a voltmeter and that is what I rely on. Not the ammeter which is still in place on 2 of My Morgans. Be careful installing a voltmeter and make sure the ground is solid and adequate.