I believe so. A condition of your diversion for Oregon is to have an ignition interlock device installed in your vehicle during the year long period of diversion. However, I have seen at least one judge terminate that condition after a couple of months if everything is going smoothly. You should speak to your attorney about this.
Nothing discussed should be taken as legal advice. Posting details of your case on an open forum could be used against you, so use extreme caution. The best way to get legal advice is to consult privately with an attorney.
Your diversion requirements probably say that you must install the IID in any vehicle that you own, even if you do not drive it. If you cannot afford to install one, you may want to sell your vehicle. You may even be able to arrange for a sale contract whereby you have the right to re-purchase your car from the buyer after the ignition interlock device requirement is over.
Oregon’s DUII Diversion statute provides, as of January 1, 2012: “The court shall require as a condition of a driving while under the influence of intoxicants diversion agreement that an approved ignition interlock device be installed in any vehicle operated by the person during the period of the agreement when the person has driving privileges.” ORS 813.602(2). So it's not about putting the IID in vehicles you own -- it's simply that you can't "operate" any vehicle that doesn't have an IID installed. If you do, and you get caught (there's a notation on your driving record for any cop who pulls you over), it's quite possible you'll be convicted of DUII, put in jail, and get a 1-year license suspension. The stakes are too high -- don't do it.