Yes, you can message someone who’s blocked you on Skype. But the only problem is they will not receive those messages until they unblock you, they will have no knowledge (through Skype) that you’ve messaged them. One more thing you must know that after a certain number of days, the message automatically gets lost, so if you’re not unblocked before then, they’ll never receive the message.

Well, if someone’s blocked you take the mature path and stop harassing and bugging them. And yeah you can also create a different account (against terms of service) and attempt to reach out, but then again they can always block that account as well. So yes, you can send messages to someone who’s blocked you, but until they unblock you, they are not actually receiving the message or receive notification of the message.