I've done that several times on my annual London trips. The advantage of the Piccadilly line's rolling stock is that extra space has been set off by each central door for luggage. However, since the Piccadilly line stop by my hotel (Russell Square) requires going up steps followed by a lift trip, in more recent years I've switched over to the more expensive (but way faster) Heathrow Express followed by a short-ish cab ride from Paddington.
If you’re traveling from LHR to central London,
http://www.blackberrycars.com£39 for airport pickup and drop-off at most central area hotels. £30 for hotel pickup and ride back to airport. If you’re traveling with a companion and don’t book your HEX tickets 90 days in advance, it’ll be £44 plus your tube fare. Even booking 90 days out, it’s still £24 for two HEX tickets plus another however much for the tube and it’s totally worth it to me to pay a little more and have a nice car service and not have to drag my bags through Paddington Station in the middle of the morning commute rush.
