Andy,
First things first, I strongly encourage you to move over entirely to PI and stop using CCDStack. You get much more control and far better results in PI. I have a cribsheet that walks you through all the details if you are interested. Just send me an email at jkmorse57@gmail.com and I will be happy to send it along.
As to TIFFS, the downside risk is that you will want to be in 32bit space as you process your images. I know Photoshop works in Tiff space, but you are losing depth of image which as a part of processing often well exceeds 16bits. As such, once you get those images into PixInsight and working, convert them to 32bit floating point files as soon as you can, preferably in the .xisf format (though straight 32 bit floating point FITs works as well).
Only other thing you are surrendering is the information in the FITs header which is all lost when you convert to TIFF. No a terrible loss, but something to consider. Note I have tried to help folks experiencing this problem in the past. Check out this post:
http://pixinsight.com/forum/index.php?topic=8021.msg52728#msg52728Best,
Jim