Isp reprogramming of Attiny167 MCU while soldered in a circuit is possible?
According to the datasheet, yes, it should be possible if set up correctly:

21.8 Serial Downloading
Both the Flash and EEPROM memory arrays can be programmed using the serial SPI bus while RESET is pulled to GND. The
serial interface consists of pins SCK, MOSI (input) and MISO (output).
After RESET is set low, the Programming Enable instruction needs to be
executed first before program/erase operations can be executed.

(emphasis mine)
You will need to pull RESET low by connecting to ground. The USBasp should automatically accomplish this (see NStorm's answer).
I'm not sure if the arduino IDE performs memory verification using read instructions during the programming process or not, but regardless, MISO should operate just fine as an output when pulled to ground with a 10K resistor (this is generally ideal for any pin operating as an output).