No

Almost all of the sUAS aircraft use a barometric altimeter module for altitude measurement. Typically when you first takeoff, the pressure in millibars (mb) is considered "zero feet". No matter how high or low you go, zero feet is where the aircraft launched from. Unless you are wealthy enough to afford a radar altimeter, your drone does not know your altitude above changing terrain.

# Is GPS Altitude Accurate?

The GPS data that you see in the On-Screen Data (OSD) are raw data from the GPS receiver. You can see variation of as much as 100 ft in just a few seconds. THIS IS NORMAL. The average reading may well be hundreds of feet from the actual physical altitude in MSL. Again, THIS IS NORMAL. On the latter, the math behind this error is way beyond my pay grade, but basically, the Earth is not round and the satellites' orbits are not "smooth" because of variations in the gravity field. Then add the problem of relativity because the atomic clocks in the satellites run slower than the same clocks on the Earth.  Altitude error is specified to be 1.5 x Horizontal error specification. This means that the user of consumer (non-military) GPS receivers should expect +/-23 meters (75ft) with a DOP of 1 for 95% confidence. Altitude error is always considerably worse than the position error. Much of this is a matter of geometry because vertical position relative to the satellites is extremely small.
On the former, why does the altitude readout jump all over the place when at rest and my GPS in the car doesn't? As explained above, the math for altitude is looking at data from at least four satellites that are constantly moving relative to your position. A change of a billionth of a second from one reading to the next will generate a different altitude. Your drone's OSD is showing you the real-time data. Your car GPS, on the other hand averages the altitude readings over a few seconds (ten-seconds in my Garmin Nuuvi), so it appears to be stable. Almost any calibrated barometric altimeter will be more accurate at reading altitude than a GPS.
Manned aircraft can use GPS for landing guidance in instrument contitions, but the FAA still requires a barometric altimeter for the final approach even in aircraft equipped with Wide Area Augmentation System (WAAS) equipment.
AC 90-107, Page 12:  "The vertical guidance is advisory only and pilots must use the barometric altimeter as the primary altitude reference to ensure compliance with any and all altitude restrictions during instrument approach operations. "The vertical guidance is advisory only and pilots must use the barometric altimeter as the primary altitude reference to ensure compliance with any and all altitude restrictions during instrument approach operations.