Hopefully my question is self-explanatory. For example, I purchased some ether on Poloniex today. Within what time frame is that transaction likely to appear on etherscan?
Your transaction will appear on etherscan once you withdraw your ethers (or DAO) tokens are withdrawn from Poloniex. The transaction will be from Poloniex's Ethereum account into your Ethereum account.
Prior to your withdrawal, your ethers (or DAO) are stored as entries in Poloniex's internal database.
When your withdraw from Poloniex, you will have to click on a confirmation URL in an email sent from Poloniex to your registered email address. Only after this URL is clicked will your withdrawal transfer take place.
Your Poloniex withdrawal history will have a transaction hash - you can use this to trace your transaction on etherscan.