My first touring bike was a cheap hybrid that introduced me to cycling in 1997. It served me extremely well until it was finally stolen. I then adapted a cheap hi-ten steel-framed mountain bike with front suspension as my next tourer. It served me very well.
The MTB was replaced by a Fuji Touring. I've also toured on a Ti framed road bike, which also has towed a trailer. And I now have a Thorn.
But if I wasn't able to afford to ride a dedicated touring bike, and my original hybrid was my only option, I would still use if for touring.
One thing, though. Put some bar extensions on it, or replace the handlebar with bull-horn bars or butterfly bars, just so you have additional hand positions, rather than just using the straight bars.
Replacing the front fork is not necessary if the only reason is to save weight. Even when doing inn-to-inn touring without camping, the weight is not going to be a significant issue.
Good luck with your touring adventures.