No. The HSC will not create any HIVE infact it will end up burning some of the collected HIVE in order to help combat the main chain inflation.
Unlike ETH now, HSC will get it's block reward from the HIVE gas fees paid by the user interacting with the HSC or deploying contracts. The network won't create nor inflate any HIVE. :)
The PoW is there to encourage decentralization and pay out future miners some HIVE. But the Hive the miners receive won't be 100% of the HIVE gas fees paid by the sidechain user. Instead that miner payout probably looks something closer to 65%-75% with the rest being burnt or forwarded to the future R&D fund.