No. If you move the stick, you'll change the speed.
If the aircraft is trimmed properly, then by slowly adding and reducing power, the a/c should climb and descend whilst maintaining roughly the same speed. Big changes in pwer setting will have an unsettling effect and the speed may change dramatically.
A glider can only maintain a constant airspeed and constant alt if in an updraught, basically the vertical movement of air is adding energy into the system. What we power pilots do by burning some fuel.
DFC, I do know it's a rhetorical question, but I couldn't help myself!