I would say yes, although I think of the word “conscious” as an adjective corresponding to having some threshold level of a continuously ranged property called “consciousness”, and so as not being well defined until that threshold level is specified. The reason I would say “yes” is because I interpret the word “consciousness” as referring to a property of information processing systems which corresponds roughly to the extent to which the information being processed includes a description of the internal state of the processor (which of course can never be 100% for a finite system), and I see no reason why a brain in a vat should not be able to process (ie “think about”) some aspects of its own thought processes. This might be more difficult if the brain had never been given any external data to process, but if it had any prior contact with an “external world” then I don’t see why it could not continue to think about those experiences – and also to think about what it had been thinking.
Source: Can a ‘brain in a vat’ be conscious? | Scientific American