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This article is from the Star Trek Tech FAQ, by Joshua Bell inexorabletash@hotmail.com with numerous contributions by others.

06 "What about beaming things off the Holodeck (ala "Ship In A Bottle" [TNG])?" (Holodeck and Computers - Star Trek)

This has never been tried, as explained in the episode, which is why
the computer was unable to simulate the results. Replicated objects
should be able to be transported out of the Holodeck, but anything
relying on the force beams would instantly collapse.

As for uncoupling the Heisenberg Compensators - that would give a
random quantum state to each particle in the transported object. It
would be akin to a molecular-resolution transport - probably deadly
for any living being.

 

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