When applicable, yes. Sometimes they're very limited, such as a Thief can take Core Utility powers, but could not replace one of their "Tricks" with a regular Rogue At-Will.
But many of the entries, such as the Sentinel, say something to the extent of "Choose an at-will. Here are five, in case you own no other books."
The character builder is usually my go to, if it's terribly unclear what's allowed. If you click the "Show additional Options box", it'll let you pick from the rest of the class' powers, if it's permitted.