The short answer
Not really, and you need to know what you're measuring your "altitude" against.
Longer answer
First let's define altitude and elevation. The two terms have slightly different meanings, and their exact definition does vary depending on your reference source. However, altitude is generally used to refer to height above the earth's surface. Elevation is generally used to refer to height above a given datum. As an example, a village on a mountain may have an elevation of 1500 metres above sea level, the most common datum used for measuring elevation. An aircraft flying by might be at an altitude of only a couple of hundred metres, if the pilot was using a local airfield and measuring altitude that way, or maybe 1700m if he was using something close to mean sea level, or something different again.
Now we have definitions out of the way, we can examine how GPS receivers measure elevation (or altitude!)
GPS receivers have an in-built, idealised, model of the earth's surface and they generally measure their elevation from that. This model is called a geoid and may be, or may be not, close to mean sea level which is probably where what maps and other elevation definitions use. So if you want to use your receiver to check your elevation against a map, ensure you baseline your receiver's elevation display against the map to see what the difference is. This won't be consistent over a very large area, say 100km+, as the distance between the geoid and mean sea level does vary. Mean sea level itself does vary from place to place too.
The other point to consider is that GPS is designed for horizontal, not vertical accuracy. The vertical error is likely to be 1.5 time that of the horizontal EPE.
There are some GPS receivers have built-in barometric altimeters, which function like those fitted to aircraft. The altitude/elevation that these units display will vary according to the pressure setting, and the reading may or may not agree with any conventional GPS receiver.