Besides the risk of either inducting more dirt into the maf through the air filter, it could also vibrate loose/ out if its not securely held in place.
There is a slot in the lower air box where the filter sits to contain it between the MAF and the filter housing while closed, but the seal is less effective when the lid is removed as that takes away half the seal. The aftermarket air intake systems tend to clamp the filter onto the MAF for this reason (that they don't have any other attachment feature/ retention feature for the filter).
So the major risks are of engine damage, the chance of this happening is hard to predict since I haven't tried running with the lid off.
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