This is the same question as the NPPL (both LAPL and NPPL are sub-ICAO). I'm not sure if there was ever an official conclusion from the FAA about the NPPL, and so the general advice (from the NPPL website) was that it hadn't been allowed.
However I normally go on the basis that if it doesn't say no, nothing stops you
They did say that they accepted the non-ICAO IMC Rating in the UK as an equivalent to an IR (
License Privileges, Aircraft Registers, Etc) so I suggest that they could use the same principle for this.