Hi,
From what I know - technically it is possible, as the trial version is almost identical to the enterprise version, except for the license limitation and the database used.
So if you purchase an enterprise license and move your data from the SQL LocalDB to either SQL Server Standard/Enterprise edition - it would probably work.
Maybe the BP guys can provide a definitive answer on this. I'm pretty sure though they would advise that you re-install BP using the enterprise installation distribution, as it might be safer for production use.
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Eric Scott Herman
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