Does this produce the anti-Markovnikov product because of the ROOR?
Yes, having a peroxide will change the regiochemistry to an anti-Markovnikov addition. The reason, as suggested, is because of a change in mechanism to a radical process (below). The homolytic decomposition of the peroxide initiates the radical chain, generating two hydroxyl radicals. The hydroxyl radical abstracts a hydrogen from HBr to give a bromine radical. This is where the cycle really begins, with bromine radical adding to the terminal end of the alkene, leaving a radical at the internal position. The stability of a tertiary radical relative to a primary radical drives this selectivity. The tertiary carbon radical abstracts a hydrogen from the next molecule of HBr, giving the product and a new bromine radical which reenters the radical chain.