If you don't chase when you need to, you'll have a very tough time threading the bottom bracket in, and as a result, it may creak or wear out somewhat faster than it would otherwise.
The same goes for facing the bottom bracket shell.
This is what I would do (and have done) if I were in your position, only for square taper, cartridge bottom brackets*: Since you are using a square taper bottom bracket, your BB will likely have one fixed and one free cup (or whatever its called). Take the free cup, and thread just that into the shell without using any tool besides the driver (example), only finger tightening it. If you can thread that all the way in until its outer flange is flush with the shell, then your frame is "good enough" as it is. Unthread the free cup, and install the BB properly and you should be good to go.
If you can't get the free cup all the way in without using tools, then I would have the threads chased out.
I used this method on my Surly Cross-check frame in 2007, and the threads were good enough then, and I haven't had any bottom bracket troubles whatsoever.
And cough up the extra cash to get the better bottom bracket, it will last longer, and every time you have to take square taper cranks off, you wear them out much quicker.
*Hollowtech and other outboard bearing systems are more sensitive to the threading, and especially the facing of the shell. If using those systems, always have the bottom bracket faced, and at that point you might as well chase out the threads.