The short answer to the OP's query is a simple "NO," or at least "NOT LIKELY."
But I understand the difficulties some face, the accompanying anxieties, and the drive to grasp any straw of hope. So I made, as I often do, an effort to illuminate the improbability (close to impossibility) contextually, with explanation.
Moreover, "no" is not actually correct. It is possible that a request for urgent processing could result in an expedited oath being scheduled. This is so NOT likely as to practically be a "no," but "no" and "not likely" are not equal, not the same thing.
In the meantime, especially in this forum of late, "not likely" tends to be sometimes be misunderstood, some seeming to take "not likely" to mean it is likely for them, for their
special circumstances. Many times, like here, it is better to offer a contextual explanation for just how NOT likely something is. Many times, like here, this can be accomplished by noting what special circumstances might, just possibly might, make the difference between an absolute "NO" versus a very, very small possibility, the "not likely but (rare) possibility."
Not entirely related on topic, but if a new citizen needs to travel after the oath, they need a Canadian passport regardless of their other passport, since they would not be allowed back into the country without a Canadian travel document.
We do indeed see more than a few struggle with the quandary of a scheduled oath in close proximity to necessary international travel.
The solution is to notify IRCC so that IRCC can reschedule the oath, which invariably will be at a later time, and potentially significantly later. Potentially so much later that those who are anxious to take the oath will generally, and carefully, consider whether the need to travel as scheduled is a priority over taking the oath when scheduled. That is, many would be prudent to alter their travel plans in order to accommodate taking the oath.
Correct that you'd need a Canadian passport to fly back to Canada. They may let you in, but it would be quite a hassle since you're essentially breaking a law. I assume it's a law and not just a policy.
There is NO law broken by a Canadian citizen traveling without a Canadian passport.
Most Canadian citizens (not all . . . not me for example, not those who are also U.S. citizens for example) need a Canadian passport to obtain a boarding pass on a flight destined to Canada. Airlines have the final say in whether to allow boarding without displaying a valid Canadian passport, but recent reports in other discussions suggest the airlines are being fairly strict in applying the eTA related rules, at least as to Canadians with PR status, and I'd guess likewise for Canadians who are citizens as well.
No law is broken if the Canadian citizen is allowed to board the flight. But the odds are the airline will NOT allow boarding for the Canadian citizen who does not present a Canadian passport.
If, however, the airline allowed the individual to board the flight, that is OK. No law broken. No problem entering Canada upon arrival at the PoE.
The Canadian citizen who can travel via the U.S. and then travel by private vehicle to the border will have NO problem entering Canada.
Otherwise, a Canadian citizen abroad without a Canadian passport can apply for a special travel document from the appropriate embassy and there should be NO problem obtaining that . . . subject, of course, to proof of identity as a Canadian citizen, and subject to the delay this can involve, particularly in some embassy locations around the world.
Reminder: Canadians are entitled to enter Canada when they arrive at a PoE to enter Canada. This is true of Canadian citizens and Canadian PRs. This is a Charter Right for Canadian citizens. And a statutory entitlement for Canadian PRs.