Raw seems clear that this cannot be done. Assault is not on the list of legal options for declaration with an Impetuous order. I wonder though if this isn't worthy of an Errata, since it certainly seems like impetuous models with Assault not only should be allowed to Assault, they should be forced to. I'm not sure what the correct process is for submitting items to be considered in the new FAQ workstream alluded to here, but I hope this forum post will suffice.
I’d like to point out that there are two different notes on the Assault skill page concerning consequences caused by Assault being an Entire a Order skill. I’d like to counter that Assault appears to be deliberately designed so that you can’t use it in the Impetuous Order. REMEMBER When declaring Assault as an Entire Order, you must declare both the Short Movement Skill Move and the target of the CC Attack before the opponent declares AROs. IMPORTANT! Measuring Assault When a trooper declares Assault as an Entire Order, players must check whether the target is within range of the Assault charge, that is, the sum of the two values of the user's MOV Attribute, by measuring immediately after the Assault declaration is made and before the Reactive Player declares AROs. If the distance to the target is bigger than the sum of the two MOV values of the user, then the user will only Move the distance and trajectory declared.