Does inversion of configuration necessitate reversed optical rotation?
if optical rotation of optically pure 2-bromobutane is some (+X)
  degrees, will optical rotation of the product be some (-Y) degrees?


No, there is no correlation between the configuration at a chiral carbon and the sign of optical rotation.  

For example (from the Aldrich catalogue), the following chiral bromo compound, (R)-(+)-2-Bromo-3-methylbutyric acid, 



has an optical rotation of [α]22/D +21°, c = 37 (c is the sample concentration in grams/100 ml solution) in benzene.  The inverted hydroxyl analogue, (S)-(+)-2-Hydroxy-3-methylbutyric acid,



also rotates light in the (+) direction.  Its optical rotation is [α]20/D +19°, c = 1 in chloroform.