Rushing for WRs, TEs, and QBs is determined by the player's Rushing Stamina rather than your playbook. If you have no one on the field that has a high enough Rush Stamina, you will pass regardless of what the playbook says. Occasionally, you will get a WR or TE rushing, but it will be randomly determined based on game situations and your players' Staminas. Having more WRs with higher Rush Stamina will increase the chances and number of WR rushes, but never above 2 or 3 a game.
If you have a player that ran at RB-type levels, like Bobby Mitchell or Charley Taylor, they will participate in rushing plays. So in the case of a no-RB formation with one of these guys on the field, you could set them up to run. However, it will still limit the rushing if they are going over their pace.