No, you can only claim the foreign housing exclusion as part of the foreign earned income exclusion. Do you pay tax in your country of residence? Have you considered using the foreign tax credit instead of excluding your income so that you would then have earned income to allow your contribution to the Roth?
CAUTION: If you elect to switch to the Foreign Tax Credit, and you have taken the Foreign Earned Income Exclusion in prior years, this amounts to revoking that exclusion which bars you from being able to take the exclusion again for a period of five years without first seeking permission from the IRS. Permission from the IRS requires a Private Letter Ruling, which has a filing fee of $2,000.
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