I would say yes, you can. At least, I can't find anything prohibiting that. Step 13 of the Eternal War mission pack is "Resolve Pre-Battle Abilities" which states
BRB, Page 282 wrote:Players alternate resolving any pre-battle abilities units in their army may have, and resolving any Stratagems that are used before the battle (excluding those that upgrade their units or those that enable them to set up a unit in a location other than the battlefield), starting with the player who will take the first turn.
so you would use the Diabolical Soothsayer ability as your first Pre-Battle ability , and then use your 4-6
CP on other Pre-Battle stratagems.