The voltage will not exceed 3.2V. It starts at whatever the discharged state of the battery is. The current is approximately 0.75/R3, until the voltage limits (it may never limit with two NiMH cells, and if it does, they may be damaged). The current then goes to zero. R3 needs to be about 3 ohms.
In simulation, it oscillates at high frequency. You can eliminate this by adding 100nF from base to collector of the transistor.
This still does not solve the problem of accurately determining when the charge is complete, as has been noted by others.
NOTE: I'm not endorsing this circuit, I'm just explaining how it works.