Is it possible to query GZIP document stored as Binary data in SQL Server?

I have about thirty-thousand Binary records, all compressed using GZIP, and I need to search the contents of each document for a specified keyword. Currently, I am downloading and extracting all documents at startup. This works well enough, but I expect to be adding another ten-thousand each year. Ideally, I would like to perform a SELECT statement on the Binary column itself, but I have no idea how to go about it, or if this is even possible. I would like to perform this transaction with the least possible amount of data leaving the server. Any help would be appreciated.