Yes, a pool can mine through another pool. There are pools already doing this as you can see under the "proxy mining pools" heading of the mining pool list at https://bitcointalk.org/index.php?topic=104664.0
You won't control which transactions go into the blocks or be able to vote directly with the hashpower. You'll be providing hashpower to another pool that decides how to use it.
The technical part of proxying
If the upstream pool allows you to mine with a larger extranonce2 size than the regular 4 bytes, then you could use a single connection to the upstream pool and partition up the work you receive for your downstream miners with extranonce2 size of 4 bytes. If the upstream pool does not allow this then you'd need to create one connection to the upstream pool for each downstream miner and just pass the work data through like a plain proxy.
In either case you'll need to observe work submitted by your miners and whether it is accepted or rejected by the upstream pool.
Having one upstream connection per downstream miners means a lot of connections. But it simplifies counting accepted and rejected work for your miners, as upstream and downstream difficulty would be the same. You just pass everything through and watch to see what is accepted or rejected by the upstream pool. If you are mining on a single upstream connection then you'll be mining at a very high difficulty in the upstream pool. You can't have your miners all mining at that high a difficulty. So you'd need to process the lower difficulty work that does not meet upstream difficulty yourself instead of passing it upstream for acceptance/rejection. Whenever work from low difficulty miners do meet the upstream difficulty, then their work must of course be passed upstream.
You'll probably want to contact the upstream pool ahead of time. If you create 1000 connections to their pool from the same IP address there could be problems.
If you use the PPS reward system things are pretty simple (but extremely risky). If you use something else then you'll need to think about whether it is safe from pool hopping or not. I'm not sure if anyone has ever analyzed whether you can pool hop a PPLNS pool that proxy mines another PPLNS pool, for example.