Yes, committing both actions is not only OK but preferable when appropriate.
Voting of any kind should be made in the interest of maintaining a high-quality site of accurate and on-topic biology information. Voting is not meant to relate at all to personal judgements or individual punishments (and as such any discussion about ethics, double jeopardy, etc. is just not in alignment with the purpose of these privileges).
Building off @Chris's answer:
You have to remember that the purpose of the Stack Exchange websites are not strictly to answer people's questions. Instead, (as stated in our Tour for example) the purpose of this site is rather to build a repository (i.e., a "library") of detailed answers about biology. The goal is to maintain a high-quality source of such information.
As a result, neither general voting (up or down) or voting to close should ever be made from a personal standpoint but only from the standpoint of maintaining a clean and high-quality site of biology info.
(This is reflected, by the way, in the purpose/action of moderators -- mods are not here to "police" people's action as much as mods are tasked to maintain high-quality community and post standards that adhere to the previously decided-upon standards of the community and SE network as a whole)
It would be very useful if all (or at least more) community members knew our guidelines and voted to close posts that fail to meet the site's standards. (However, individuals should only vote to close posts that properly qualify for such voting). In fact, SE sites are meant to be moderated primarily by the community (and only secondarily by mods).
If a post is bad enough to vote to close, it likely qualifies for a downvote as well*. (Because, remember, the purpose here is for the community as a whole to maintain high-quality posts).
Downvoting in conjunction with voting to close has the added benefit -- as @Chris mentions -- of helping the system to eventually delete low-quality posts automatically after closure.
It also sends a strong signal to other users who are new or otherwise less familiar with the site's standards that the post is not the quality the site is looking for. This is especially important since many posts linger in the VTC queue for some time. Downvoting helps to stand-in during this time to send the message to the OP as well as to try to convince other users not to "waste time" answering the post without some adjustment from the OP.
*From my own personal perspective, I don't think downvoting good questions is necessary if they meet all of our criteria except that the question would be better fit on another SE site. I understand why some people do it (again, to send a clear message of what's on topic and what's not), but I don't vote these posts down. If they truly are a bad fit, they'll likely get moved.
More generally, I personally think that any downvote or vote to close should be accompanied by a comment to help teach/remind both the OP and any other visitors or community members of the site's standards and expectations.