Nearly any bike will ride straight. with or without hands.
Witness all the neighborhood kids delivering papers on their
bmx frames, no hands and with a friend riding on the
rear pegs as well. From that example to seeing a victor throw
up his hands at 38mph the moment after a field sprint, he, atop
a bicycle most of us might consider 'factory-made', it ALL works!

However, that doesn't mean you should allow yourself to be content
with the attitude of the lowest common denominator as in, "well,
it's good ENOUGH, why spend more time on the intangibles?"
Proper/perfect/near-perfect alignment will always be better added
in, ( or built in ), than left out. If nothing else, do it for yourself,
unless that 'time versus money' issue is rearing its head.
One point worth considering, which is paramount, is that while
frames which are seemingly out-of-alignment when checked
with the appropriate tools all still ride swell, there is no getting
aound the fact that the rider over it and the parts hung on it
will wear unevenly no matter how nicely down the road the
bike goes. Premature wear on the parts AND on the rider will occur
unless the frame in question is 'straight'.
And regarding the question of ''How straight IS straight?'', it's like
you cannot be kinda' pregnant.