Early Telecasters/Broadcasters were sometimes used as bass guitars because their ability to filter treble out was so good (sic).
An effects unit/pedal will boost/alter the gain(etc) and add various effects such as mentioned by dot.dot.dot.
For example mc9mm's crappy Hondo and 5w amp put through a fairly decent effects processor will have the ability to sound like Hank Marvin in a cave or Korny guitarizt meets EVH at a very heavy metal festival in Bonkersland,given the limitations of the guitar/amp.
Effects processors are the cheaper way into getting lots of different FX for your money,but i prefer pedals as the effects in my effects box ain't that exciting/affecting..
If you listen to some Jimi Hendrix you'll get an idea of what quality pedals can do for your sound.
Effects pedal of choice..Wah..Voodoo Chile(Slight Return)....etc.
Accuracy,you say? hmm interesting concept..