"Could be flown" is a clear yes, "could be flown to a landing" is another story. Most of the points you are listing can be accomplished using the backup system in the LM, the Abort Guidance System (AGS). I'll be using the LM Apollo Operations Handbook Volume I as the main source for all your specific points.
An attitude / attitude rate reference is available to the crew (other than out-the-window)
The AGS has a subsystem called the Abort Sensor Assembly (ASA). As the AOH says, "the ASA performs the same function as the IMU" (Page 2.1-8). The ATTITUDE MON switch selects PGNS or AGS as source of vehicle total attitude and attitude errors displayed on the FDAI. The displayed attitude rates displayed are always obtained from the rate gyro assembly, which is part of the AGS. So the LGC is not the source for the rates on the FDAI (Page 3-20).
An altitude readout is available to the crew (other than out-the-window)
The MODE SEL switch switches between three source for the altitude/range indicators (tapemeters). LDG RADAR, PGNS and AGS. In the LDG RADAR position the displays show the raw LR data (slant range and rate), in PGNS and AGS mode the data is coming from the computers. (Page 3-22).
A three-axis velocity reference is available to the crew
In AGS mode only two axis are available (altitude and lateral), but the raw data from the LR is showing altitude and altitude rate on the tapemeters and forward and lateral velocity on the X-Pointers. (Page 3-16, X-Pointer indicator, Remarks).
The crew can manually control the attitude of the vehicle
The PGNS and AGS have automatic attitude control modes, but there always is a capability to control the attitude manually using the Attitude Control Assembly (ACA) in different modes, from computer aided to full manual hardover (Page 2.1-30, all modes except Automatic).
The crew can throttle the descent engine
Manual throttle commands can be generated using the Thrust/Translation Controller Assembly (TTCA) which always are added to the auto throttle commands from the LGC (Page 2.1-20, first paragraph).
The crew can shut off the descent engine
This can be accomplished using the engine stop buttons (Page 3-81, Engine stop pushbutton and Page 2.1-140, figure 2.1-51).
What the AGS does not have is the descent guidance programs of the LGC. So landing without the automatic guidance is probably possible by following a nominal altitude and altitude rate chart or so, but landing with any accuracy at the desired landing site without the LGC would be rather difficult.