Is it possible for any reason that your wallet gets blocked?
Yes,i too don't think that it could happen.Only one issue with the wallet would be that if you miss your private keys.But while using the wallets,we should first ensure that we really download wallet from the official website or not.For example,recently when hard fork happened and new BCC coins were created and many got free BCC coins equal to the number of bitcoins,one person has downloaded a wallet from Electrum cash.com which was later changed to Electron cash.com.He has lost his 40 bitcoins since it was a wallet from a fake website and instead,he should have downloaded it from the official website Electrum.org.
i think you missed the question, i think the op was trying to ask if his transactions from his wallet could be prevented from being processed, not if his wallet could be compromised.
and yes, it can. to my understanding, if big pools and miners set it so that transactions originating from addresses known to be contained in your wallet (technically, it would only have to be addresses containing the coins you are trying to spend in a particular transaction) then your transactions would not be processed. however, if a miner or pool not blocking your addresses were to find the block, and your transaction was included in that block, it would be processed. this (again, to my understanding. someone can correct me if im wrong) is the same idea that allowed the services that sped up transactions to work.