Automatically inferred invariants have been found to be successful in detecting regression faults in traditional software, but their application has not been explored in the context of spreadsheets. In this paper, we investigate the effectiveness of automatically inferred invariants in detecting regression faults in spreadsheets. We conduct an exploratory empirical study on eight spreadsheets taken from VEnron and EUSES corpora. We apply automatic invariant inference to them, create tests based on the inferred invariants, and finally seed the sheets with faults. Results indicate that the effectiveness of the inferred invariants, in terms of accuracy of fault detection, largely varies from spreadsheet to spreadsheet. The effectiveness is found to be affected by the formulas and data contained in the spreadsheets, and also by the type of faults to be detected.