It is, clearly, GM's Option. But that said, I'd always let people use encounter/daily powers for less than the full effect to get a side effect (this is NOT a "bag of rats" option, as they're expending resources), particularly on the effect line.
If they're using the power in combat, great -- they are choosing to burn something that -could- be used for an attack for less than the full effect. If they are using it in a Skill Challenge, -great!- -- using powers and creativity in skill challenges should be rewarded, not punished (and if you're willing to use, say, the Avenger Daily Aspect of Might in a skill challenge for +5 to Athletics rather than waiting to get a 3w attack and +2 to melee damage in a combat encounter, have fun). If it's in a roleplaying challenge, well, why the hell not?
The same for using normally triggered teleports and such. It's not out of line for the GM to overrule these, but the "say yes" rule -very- much comes into play here.