Yes.
Citizens United had nothing to do with how a candidate finances his or her campaign. It dealt with independent expenditures by corporations--i.e., expenditures on political speech relating to a candidate that are not coordinated with a candidate. (Of course, my answer assumes that whatever is done merely overturns
Citizens United, and doesn't go further by, for example, authorizing Congress to make any and all campaign-finance laws it wants to, notwithstanding other provisions of the Constitution.)
NYCmetsfan is right that what matters here is
Buckley v. Valeo, not
Davis. In
Davis, the Court considered whether it was constitutional for the government to increase the contribution limits for contributions to a candidate running against a self-funded candidate who spent above $350,000 of his own funds on his campaign. If you read
Davis, you'll note that the Court even cites
Buckley for the proposition that a "candidate
has a First Amendment right to engage in the discussion of public issues and vigorously and tirelessly to advocate his own election." In
Davis, the Court simply recognized that the one-sided contribution-limits increase imposed an (unjustified) substantial burden on the right recognized in
Buckley, and was therefore invalid.
In summary, overturning
Citizens United would not, on its own, affect whether a candidate can self-finance his or her campaign. Those are two completely separate issues.
