Only in the most limited ways.

First check there is no DC offset - if you find more than 50-100mV  go recheck everything, esp. the signal and power grounding.*

The only way with a multimeter of checking that the amplifier is doing its thang would be to run a 50Hz test tone (use Cooledit or similar, burn a cd or link to soundcard and run the file) and check that you get an AC voltage reading on your multimeter that varies 0- approx. 0.7*rail voltage from the output of the amplifier as you vary the volume control across its range.

NB this last test is crude; multimeters (unless you've spent the equivalent of a small amplifer on it) are average-responding, not true-RMS. It's a good approximation on a 50-60Hz signals (since such meters are most likely to be used on the mains) and fairly close over the range 50-400Hz, presuming a true sine output. (* Because of the averaging it may be that the multimeter reports a small DC offset as a result of aliasing the HF switching noise on the output of a Class D amp - I don't know, 'cos I haven't tried it; but less than 100mV and you should be safe to test it with a real speaker). The multimeter can tell you nothing about quality though

Now hurry up and finish the project, we all want to know what it sounds like