Yes, an engine with points/dwell style ignition will run without the condenser, but it will run poorly.
The condenser does more than just protect the points from burning up, it also prevents run on contact (arcing) when the points start to open. This causes the ignition event to be late. It also happens at less predictable times.
To run without the condenser, you'd have to change the timing a bit to account for this.
Don't believe me? Disconnect the condenser while it's running and listen to it stumble. Better still, put a timing light on it and watch the line dance around with increased timing variance.
As for the original question, I think it's been answered. The points are either acting as a low voltage switching device with no condenser required, the condenser is mounted somewhere other than near the points and it hasn't been located yet, or it was left out at the last service.
Jason