"The coat is not in the restaurant."
Translation:Der Mantel ist nicht im Restaurant.
Yes. In fact I have verified this with a friend who is a German teacher in Germany. She told me that it is perfectly acceptable to use the individual words (in this case, 'in dem') instead of the contraction. Just like it is acceptable to say 'can not' instead of 'can't' in English.
"in dem" ist gramatically the long version of "im" so it should be correct...