Well I've never tried it, Peter, so I'll bow to your experience.
For interest, I took my reference from the INS troubleshooting table in the L1011-500 operating manual under 'abnormal procedures'.
A drill is given for a situation where the ADI has tumbled, and flags are in view on the ADI, HSI and RMI. The INS CDU warning light is ON showing action code 1, a platform problem, and malfunction codes 37, 38 and 39.
The diagnosis is a system overheat with the MSU in NAV.
The drill is to select the MSU to OFF, flight or ground. If a single INS has failed it is left OFF and referred to the engineers after landing. If both INS in a two INS system are affected, check the equipment cooling. If the cooling was off and is sucessfully restored wait two minutes and, in flight, select ATT. Fly level until ADI flages retract and ADI is level. If the CDU warning light comes on again turn MSU to OFF and leave it off.
The existence of this drill suggests to me that the INS is capable of detecting an approximate gravity vector in level unaccelerating flight.
The drill I found in the B737-400 Flying Manual is 'IRS attitude failure after generator failure'
'If neither IRS attitude display recovers after a generator bus is restored:
IRS Mode Selector Switches...................................ATT
Maintain wings level, constant IAS for 30 secs
Magnetic Heading..................................................ENT ER
Enter heading on either FMC POS INIT page or on overhead IRS display by selecting HDG/STS.'
The 737-400 Technical Manual also says that ATT can be selected and the system can be coarsely re-aligned in the air following loss of both DC and AC power.