It doesn't matter whether you've downloaded the file, if it's not installed on your phone before Apple stops signing install requests you WILL NOT be able to install it on your phone. Any time you install iOS on a phone, it MUST phone home to Apple for permission. If you wait until after 5.1 is released you will ONLY be able to install 5.1.
That doesn't sound right.. I was successfully able to install 3.1.2 on my iPhone 3G when 3.1.3 was already out, as I had 3.1.1 installed at that time. It wasn't until about 3 months later that I installed 3.1.3, which I was able to get successfully as well; so I don't know if that is the case, or if that has changed.
BL.