Is this a good thing to do, or does vocal tiredness and occasional horseness mean thats bad?
It's probably not good. You can broaden your range with practice -- Placido Domingo, for instance, started as a baritone but made the transition to tenor very early in his vocal training. But there are limitations -- Domingo started out as a high baritone, and he never lost the darker coloring of his voice that true tenors, like Pavarotti, lacked.
If you do it right, you can add a few notes to the top of your range, maybe half an octave. On the other hand, if you do it wrong, you can ruin your voice permanently. If you have a vocal coach, follow his/her advice. If you're still straining and hurting, get a different coach. You should expect results, but don't expect miracles.