So, to directly answer the question: Yes, SE does monitor voting algorithmically, but this is not the kind of behaviour that gets picked up (the system is more targeted at users trying to inflate their own reputation or that of other specific other users).
As can be seen in "Spam Voting" - Should we stop it?, linked by @404, this kind of behaviour is a contentious issue. I have gone with what seems to be the consensus best response and written a moderator's warning to the user. The text of the warning is as follows:
I'm writing in reference to your Economics Stack Exchange account.
Some users of the site have noticed that your account has very little activity besides the very large number of up-votes. Moreover, this pattern of behavior appears to have been replicated across a number of Stack Exchange sites in the space of a few days (other spend months accumulating such vote totals) and therefore looks quite suspicious.
The voting system is the main mechanism that we have available to direct attention to the best content on the site, and is important in helping users to identify wrong, low-quality, or unreliable posts. Improper use of the voting system undermines this function by distorting the information implied by others' votes. Please, therefore, refrain from voting except in cases where you have taken time to carefully evaluate the content in question.
Economics Stack Exchange moderator
Honestly, I don't think this will make too much difference. If the user's objective is, indeed, to obtain the badge then the damage is already done. Site moderators are not able to reverse user votes.