Is a recoil start (hand propping) allowed if it isn't mentioned in the aircraft manual?
You didn't say exactly what "allowed" means, e.g. do you mean approved by the manufacturer, or legal in a certain country? But if you're asking is it legal in the US (under FAA regulations), then the answer is yes.

AOPA has a nice article on exactly this question, called Hand propping: A legal primer. It says:


  There is no specific FAA regulation that applies to hand propping an
  airplane, either to prohibit it or to direct how it is to be done


But:


  The FAA contends that hand propping is a two-person operation and has
  expressed this view in the Airplane Flying Handbook (FAA-H-8083-3A)
  under the section titled “Hand propping.” Of course, this publication
  is not regulatory, but the NTSB was surely influenced by it in a 1983
  legal decision. In that case, the FAA sought to suspend a pilot’s
  certificate for being careless or reckless when, while attempting to
  start a VariEze experimental aircraft, it “got away” and ran into a
  parked aircraft.


The NTSB concluded that the pilot had violated 14 CFR 91.13 (careless and reckless operation):


  The board affirmed the administrative law judge’s finding that there
  had been a 91.10 (now 91.13) violation


That means that hand propping itself isn't illegal, but doing it wrongly and against the FAA's general procedures could get you in trouble:


  There have been at least two previously issued NTSB (full board)
  decisions and one subsequent decision that refer to these generally
  accepted procedures and precautions for hand propping. The precedent
  has been set. So, hand proppers beware; if you fail to follow proper
  precautions and the airplane gets away, the FAA might pursue action
  against you for being careless or reckless.