Yes you can. You will still have to put a CC guarantee on some of them, like anyone else. I have a room reservation and all my ADRs were made 180 days out, well except the ones I keep changing.
The only time that a dining plan comes into play when making ADRs is for CRT and the 3 dinner shows. If you have a Disney resort package with an applicable dining plan, the prepayment normally charged at these experiences becomes a cc-guarantee for the full amount (e.g. you'll get charged the full amount if you don't show or if you cancel after the deadline). Other than that, the system does not care if you have a dining plan or not.
The other caveat with ADRs is if you are staying on-site. Guests with a confirmed Disney resort reservation may book dining up to 180 days before date of check-in. At this time, they may then proceed to book up to 10 days worth of dining (this is what people mean when they mention 180+10). For guests coming in from off-site, they may book dining up to 180 days before date of dining.