Thinking about this I would not do this to my boots if I was you.
Years ago I poured suede dye in to a plastic cup and it, over the course of the day, melted the bottom of the cup. I have no idea what may happen if it soaked through to the gortex.
If you have ever reproofed them then the application of the waterproofer will not have been even. This may mean that the suede takes the dye unevenly and they end up looking blotchy and worse than they are now.