Search and rescue (SAR) missions were possible, and were often carried out. 980 aircrew (aircrew in general, not just pilots) were rescued by Aerospace Rescue and Recovery units from 1966 to 1970 (inclusive). SAR missions had a very high success rate at finding where aircraft had crashed, but could not always locate the aircrew (because they had already been captured, because they had fled to avoid capture, because they had been killed, etc.).
Helicopters were central to SAR efforts. The main helicopters used were the HH-43 Huskie (earlier in the war) and HH-3 Jolly Green Giant and HH-53 Super Jolly Green Giant helicopters specially equipped for SAR missions. The propeller-driven A-1 Skyraider was the usual choice to escort the rescue helicopters early in the war; their relatively slow speed made it easier for them to accompany the helicopters. Later in the war, jet aircraft were used as escorts; the A-7D Corsair II was a common late-war escort jet.
What was a pilot’s chance of being rescued after being shot down in Vietnam?
This is a difficult question to answer precisely, since the number of aircrew taken prisoner isn't known. However, we can answer it approximately. 509 aircrew from the Air Force, Navy, and Marines were released in 1973. There would have been about 150 Army aircrew in addition to these aircrew (estimating from the number of rescued Army aircrew), for a total number of released aircrew of about 660. If these were the only captured aircrew, then the rescue rate was 60%.
However, the number of aircrew captured must have been higher than this, since some POWs died in captivity.
There are still 1085 unaccounted for MIA aircrew from Air Force, Navy, and Marines. Adding an estimate of Army aircrew (324 aircrew), the total would be about 1409. If we assume that all of them were captured (which is very unlikely), then the rescue rate would be 36%.
Therefore, the rescue rate was between 36% and 60%, and was probably toward the top of this range. If about 20% of captured aircrew died in captivity, the rescue rate would have been 55%.
For more on SAR during the Vietnam War, see:
For MIA statistics, see https://www.dpaa.mil/Our-Missing/Vietnam-War/Vietnam-War-POW-MIA-List/