To bluntly answer the original question. It is!
The pressure as sensed by flush static ports is dependant on three variables:- altitude, airspeed and angle of attack (temperature also plays a part but has been discussed in many previous posts).
Cb and Flt Detent quite correctly state that for an increase in airspeed the sensed pressure will fall and hence the a/c will appear to climb.
As Gengis has stated the a/c manufacturers go to great lengths to try to ensure that the ports are located such that there is minimal venturi/bernoulli effect. For the lower airspeeds of, say, a 152 this is sufficient.
For the higher airspeed/Mach numbers of civil transport or military aircraft however, more accuracy is required. this is acheived during the original certification period when the a/c is basically a flying test bed. Pre-calibrated probes are fitted to the a/c such that they are mounted as far away as possible from the fuselage and any associated interference. These readings are then compared with those of the a/c ports at various airspeeds and angles of attack and used to create an algorythm within the air data computers so that the pilots will see the true altitude for any given airspeed or angle of attack. This correction is called, as ASFKAP has already said, static source error correction or SSEC.
I can say from experience that the difference at altitude can be huge. As an experiment (to trouble shoot a possible SSEC problem) with the a/c at 40,000 ft (using test equipment not in reality) we varied both the airspeed and angle of attack to confirm identical readings on both #1 and #2 systems. The difference for certain combinations of AoA and airspeed was as much as 900 ft!
This is why for RVSM ops the ADC's must be working and why the test/certification period can be so long.
Hope this helps.