No - I think making your lab. space "more official" is exactly the wrong thing to do! Much like having real chemical equipment setup in your home is seen by law enforcement as inherently drug-related (actually, a fairly reasonable assumption), a lab coat will be seen as just another sign (evidence) of organized drug manufacturing/conspiracy. If anything, when not in use, don't leave your distillation equipment set up, scatter lab. equipment around, don't store it all together in one spot, particularly not in a space clearly set up to do processing.
And keep in mind that some or many, including cannabis consumers, will view your home chemistry projects as wrong, even something that should be illegal and you prosecuted, clearly violating any local zoning or other safety regulations (not felonies), improper storage and handling of explosive/flammable materials, endangering yourself and your neighbors, etc. -- a hazard much the same as a neighbor 'cooking' crack or meth in their home.