Voltage follower/Buffer circuit as summing amp
In principle you can, but not well. 

The key advantage of the inverting configuration is the virtual earth input. This means that each input signal can have no effect on other inputs, there is no accidental cross-coupling of input signals.

Into a high impedance like your buffer, you can - not sum, but average - several inputs via a resistive network, but if you leave one input open-circuit for example, you'll find that average voltage appears on that input. So it's not wery accurate unless every input is buffered.

So other ways of providing a virtual earth have been used in the past - a common-cathode or common-base amplifier would do.