Does halogenation by phosphorus tribromide lead to an inverted product?
Yes, the haloalkane product will have the inverse stereochemistry of the alcohol that it was produced form. $\ce{PBr3}$ does this by converting the $\ce{-OH}$ into a good leaving group and providing a nucleophile all in one. This is can be seen in the two step mechanism:

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When $\ce{Br-}$ ejects $\ce{PBr2OH}$ in an $\mathrm{S_N2}$ reaction, the stereochemistry is inverted:

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