I would say yes ...
... and here's why.
It doesn't matter to the game, and it is cleverer and more rewarding to be resourceful.
It would be sad to let this be another sticking point for no-fun DM's to call foul from left field: "Oh, but did you collect all the specific insectoid spell components each day as well as your essential oils for the herbalism kit?" Nobody wants to play that kind of game for long, do they?
It's very easy to say "DM, I carry a pouch of various insects I've collected and I feed them and make sure they are well." But it's not necessary.
Lastly, the spell's wording doesn't say that the cloud of insects is vaporous, spiritual, illusory, or of only one kind of useless insect. It could quite possibly have 5 wasps in it and maybe even centipedes and spiders and one scorpion. Maybe that was someone's intent.
In most situations that fun should rule over debbie downer; this is an easy call.
Of course is should be allowed.
The RAW do not imply that it is not possible. A player should be rewarded for this clever association between the two staff uses, as well as freeing up a spell caster from being encumbered by unnecessary spell parts, for say, if recovering from being prisoner and losing all their gear and finding only this staff.
It's also an easy leap to say: "Look, the cloud of insects is harmless, and when you giant a couple of them they respond to the spell that cast it. This is at least 4th level magic happening here."
When I read the RAW of it I don't see any contradiction. It's completely dependent on wanting creative solutions in the game or not.
("a wasp isn't harmless but a use of Speak with Animals will surely circumvent having to use the staff to get a wasp....", I truly cannot abide by these other answers and believe i was -1'd by a fellow poster. I have reviewed the rules as written and my answer is infallible. thankyou very much. I can't believe some one would ask a player to bend backwards for a (expletive) hand full of natural insects. This is truly armegeddon then. And a wasp is harmless in real life, especially if it doesn't have 100 friends, or have you been stung for 25 percent of your health before. I haven't. My D&D character is not allergic. Should D&D characters have allergies and vulnerabilities to things like peanuts, bees, and perfume? I didn't think so. Is this a game for several people to cooperate or your next big chance to disapoint a small crowd of enthusiasts?! I thought so, burst that balloon for the sake of erring on the side of caution. Don't wanna let that cloud of insects take over the world after this 8th level encounter. Whoa BOY! There's 4 people waiting on the DM to allow one of their players to do something intelligent and creative, a review by all review shows it is possible, 10 minutes later the answer is no, and you think you've done a good job and not being stared down by 50 wasted minutes of existence (5x10) ??!! I think not. It is good that some one thought of this trick and should be allowed at every table. Honestly how could a DM ask their "friend" to come back when they have the money, i.e. 4 wasps, 3 spiders, 10 centipedes... only 9 centipedes? Come back when you have 10 centipeded, sucker. That's what you get for playing the game. Absolutely ridiculous, and people will take offense to a DM being unreasonable. And i take offense to this entire page of answers. They are all completely wrong and they think they nailed it, reading over the same text i did and interpreting it as the instructions for leaping over a giant chasm. Sigh. Super super sad for D&D. D&D is dead now. It's been murdered by this post and rules lawyers answering to the lobbyists of the big no fun police corporations that make laws to gain more no fun policies to waste player's time. That's where the money is for DM's i guess.
Let me ask you this. When you go to a party do you supply your own booze?
Is it a very rare, magical occurrance when you do so?
Give the guy some insects, you no fun, rules stamping, that's all you can do to have a good time is ruin other people's ideas, terrible DM.
under my breathe "tight wad".) humor