I have noticed that when the TIMER and /EN pins are grounded and the /CHRG pulled high through a pullup resistor (2K), the /CHRG pin oscillates at 10ms low and 20ms high.when a battery is absent. Can I depend on this behavior for battery absent detection? The data sheet does not describe this condition, but it is certainly useful if it is not just an anomaly.
Does the LTC4001 have any upper capacity limit, for example a fixed timeout of X hours? If not, I see no problem with your approach.
Take a look at the battery node voltage on a scope while this is happening. You should see a similar waveform. This is because, with the timer disabled, it is relying on current-based termination which is satisfied immediately when it starts charging. This causes the output to cycle as it continuously restarts charge cycles. This behavior is benign and reliable; you are welcome to use the /CHRG oscillation as a no-battery indicator.
You can also change the blinking speed by adding more capacitance to the battery node. This will slow the battery "charge cycle" completion, resulting in slower toggling.