Can the Insight operate without the IMA system ?

Yes the Insight and Civic can run without the IMA.
The only thing you lose is the 12V battery charging.
This is similar to running a regular car with a bad alternator. Drive at night with the lights on, and in 30 minutes your car stops due to the 12V battery running out of juice.
The IMA battery which is charged by the IMA controller, is the power source for the 12V charging system.
Ways around that issue include:
1. A larger 12V deep cycle battery that you charge off the grid each night could power the car with lights on, for 6 or more hours.
2. Adding an alternator to the car.
Some new input from Carl Brown on this subject:
I noticed on your website FAQ a question about running the
Insight without IMA installed. You might find it interesting that the remaining IMA components will keep the 12V battery charged with the HV battery pack removed, so long as the BCM low voltage connector is also disconnected and the MCM remains fully connected. The only catch is that 12V battery charging is temporarily suspended when engine RPM exceeds 4000.
I am presently replacing my battery pack, so I am using the Insight as a pure-gas car right now (with pretty lousy acceleration)."
WOW learn something new everyday. Thanks Carl.