Yes, like in almost every blockchain the block producers can manipulate block content and therefore block hash before revealing it to the rest of the network.
She just needs to randomly chose transactions from the pool and try to
compose a block with the favorite hash. The only limitation is to
produce the block in 2 sec. For example, she wants the hash to have
some four digits to be 1,2,3,4. Thus, she need to try (1/16)^4=64K
block creations which is easy to do as no proof of work is required.
No matter the complexity, trying different combinations to find a suitable hash, is basically the definition of proof of work… You could even argue that it is harder when the changing part is the transactions rather than simply the block nonce, but the principle is the same.
On the Ethereum, she would lose competition on block creation to other
miners but on the Polygon none competes with her during a sprint.
The BOR consensus allows for out of turn block proposal, so you could be front-runned by another proposer while trying to solve your artificial proof of work.
So, is it correct that Polygon consensus mechanism does not prevent a
misbehaving block producer from manipulating block hash?
While it does not prevent it completely, there are some incentives to propose your block in a reduced amount of time. But anyway, no matter the blockchain consensus / protocol, it is almost impossible (if not at all) to detect hash manipulation...
You cannot guarantee that two block proposers in any blockchain have the same transaction memory pool, therefore how do you detect if one intentionally included / excluded a specific set of transactions ? You cannot even be sure that the supposedly excluded transactions were ever received.
Hash manipulation itself is not an issue, if the hash is valid it only serves as a block identifier, tamper detection mechanism and as a link to the previous block. The real issue comes from developers using block hash as a source of entropy / decision variable, which they shouldn't, as block hash can clearly be manipulated.