Technically, no.. In order to physically test the SAME alert on your scanner, you'd have to have some way to transmit on the NOAA weather frequency, and if that isn't hard enough, you'd have to inject the tone code that triggers a SAME alert.
In my area, the National Weather Service tests their alert systems on Wednesday's between 11 and 12 noon. About the only way you could test to see that the SAME works is to put the scanner into SAME mode, and see if it recieves the alert. If it's in SAME mode, and the test alert is sent, and the scanner alerts, then it does work.
Try tuning to another boradcast frequency. It has been my experience that some NWS weather radio frequencies will make my weather radio alert, while others will not. Maybe it's just me.
I would elimiante the easy stuff first, by making sure you have the correct SAME codes programmed in, and making sure the scanner was indeed in SAME alert mode. Also make sure you have adequate reception for the transmitter you want to recieve. Eliminate the stuff you can control first, and then question the operation of your scanner. Not saying you scanner isn't malfunctioning, because hey, it's only man made.. But, you can eliminate some possibilities, to narrow down your problem.