Sorry, forgot to mention. You asked if you could cut and weld thicker material if you went slower.
Cutting: Yes, but only to a certain thickness, at that point you're no longer cutting, but hacking and melting. I know with me, no matter if I'm doing the work for myself or someone else, neatness always counts, when you cut metal thicker than what the tip size is recommended for, the top edge of your cut, which should be squared off, then becomes a rough rounded edge, because of the amount of heat needed to cut it.
Welding/Brazing:Yes, but there again, only to a point, If you're doing it on the job, you are probably getting payed by the hour, and to most supervisors, they want it done right, but as quick as possible.
I hope I didn't offend you with all the detail, but I'm not sure of your level of experience, and wanted to be as helpful as possible.
Again, best of luck.
Steve