Probably, but if there's a specific spell-and-feat interaction, talk to the GM
The metamagic feat Extend Spell does not say that it only doubles a spell's formal duration (i.e. the duration that's printed in the spell's header material). Instead, the Extend Spell feat's description says, "An extended spell lasts twice as long as normal," but "a duration of concentration, instantaneous, or permanent is not affected." Thus, if some aspect of the spell expires after a timed duration then that spell should be eligible for the Extend Spell feat and, if the spell's so modified, those aspects last twice as long.
A magic circle against… spell modified by the Extend Spell feat, for example, should either last twice as long as its header-material-listed 10 min. per level or last twice as long as its alternative, in-its-description 24 hours per caster level, depending on the option the caster picks when the spell comes into effect. (To be clear, the caster needn't pick which duration to double if a spell has multiple possible durations.)
I say should because, even though I can't see any other way of reading the Extend Spell feat, if a player has some far-out schemes for his PC—like the PC wants to create monsters or teleport at will forever—, and the Extend Spell feat is part of those schemes, then the GM may be more cautious and rule that—clearly contrary to the feat's description—the Extend Spell feat only affects a duration printed in the spell's header material. (To be fair, were my hypothetical GM to suddenly make such a ruling, then I'd be mildly annoyed, but I can't imagine leaving a campaign over that ruling alone.)
With or without such a restrictive ruling, I can imagine a GM making a distinction between the spell's effects lasting twice as long and the spell's side effects lasting twice as long due to the Extend Spell feat. For instance, the stinking cloud spell has a duration of 1 round per caster level—that's how long the magic fart lingers—, yet living creatures that fail their Fort saves against it "become nauseated. This condition lasts as long as the creature is in the cloud and for 1d4+1 rounds after it leaves." A GM could rule that a creature does not suffer from that condition twice as long (i.e. 2(1d4+1) rounds) if the stinking cloud spell's modified by the Extend Spell feat. (Likewise, I wouldn't show up at a table expecting the GM to rule that damage dealt by a freezing sphere spell modified by the Extend Spell feat takes twice as long to heal naturally with time.)
In short, if there's a specific interaction that you're curious about, I'd urge discussing that exact interaction with the GM beforehand instead of just taking it for granted that it'll work the way you want it to during actual play. While your GM may have said that a spell will just last twice long if it's modified by the Extend Spell feat, assuming that ruling means that absolutely everything about a spell that could even vaguely be considered timed will last twice as long if the spell's modified by the Extend Spell feat is risky and unwise.
