The answer is both yes and no. In principle, longitudinal/panel data can be run through BayesDB, though BayesDB would have to infer the temporal structure. Also, we've toyed a little with forecasting by making a table where each row is a sliding window.
That said, BayesDB is really about the classic multivariate statistics setting: each row is a sample from some population. We think that a streaming Bayesian database, that models sequences of timestamped UPDATEs to a DB (and with FORECAST in addition to INFER) is an interesting, distinct project that we've done a little work on.
Contact us if you're interested in this kind of data and we'd be happy to talk more.