Microsoft ICE generally does not use a lens database for automatic barrel-distortion correction. In practice, ICE already warps images as part of alignment and blending, so mild lens distortion often isn’t a problem.

A good approach is to try stitching the original files in ICE first. Pre-correcting in another program can reduce image quality slightly and may crop the frame edges, which also reduces overlap between shots and can make stitching harder.

If ICE fails to stitch well, or if distortion is causing obvious problems, then try correcting the images first and stitch again. The key is to avoid unnecessary preprocessing unless the uncorrected files give poor results.