No, it is not possible because the direct outs are located post gain and pre insert/processing. This is the way the board was constructed. You are feeding your band with plain, unprocessed signals.
What about using the 14 auxes of your board (or some of them) as feeds for the Avioms? This would give you the advantage of using stereo mixes (f.e. drums, keys) instead of individual signals - with all processing (graphic EQs, parametric EQs, Compression, Limiter, Reverb/Delay) included.