Can you legally sign a document as a patient in a hospital while on morphine drip and other pain meds, even if the hospital is stating you were coherent at the time?

The answer to your question is maybe yes, maybe no.  Anyone can sign a legal document so long as they have capacity to do so.  In most states, capacity depends on the circumstances and, so long as your Dad knew what he was doing, he probably had capcity to do it.  His capacity may have been diminished by his illness and medication, but that does not mean he can't sign documents.

The other question is the actions of his "friend."  Taking advantage of someone can make the document invalid.  There are various legal doctrines that cover this - such as undue influence, coercion, breach of fiduciary duty, unjust enrichment, fraud, or even theft. 

If your Dad wants to get his personal items back, he should speak with a lawyer to find out what can be done, at what cost, and with what chance of success.  If your Dad is a senior citizen, your state, like Florida, may have special laws that protect seniors.  Your Dad may be able to use these laws to get his property back.

If you, rather than your Dad, want to get your Dad's property back, you have to think carefully about this.  Consider what your Dad wants.  If he disagrees with you, I would expect you to lose any effort to recover the property.  If he agrees, then you can help him recover his property.