No, the tropical wind anomaly often changes on a quicker time scale than the 2-3 months it takes for the Kelvin wave to cross from western to eastern Pacific Ocean. That means that a spell of westerly wind anomalies may produce a downwelling phase of a Kelvin wave but end long before the wave makes it to the eastern part of the Pacific basin. Another spell of wind anomalies may sometimes occur while tthe Kelvin wave is still traveling eastward. This can trigger two separate Kelvin waves, or, if the wind spells are close together in time, the two spells of westerly wind anomalies may cause a single, but less sharp, downwelling Kelvin wave. The Kelvin waves are somewhat integrative--they may contain the effects of more than one spell of wind anomalies. The heat content of the subsurface waters is yet even more integrative, as it can be a result of more than one Kelvin wave at a time, such as two of them moving eastward but separated by 1000 km, being triggered by separate spells of wind anomaly. In addition to these shorter-lasting wind anomalies, long-lasting ones may come about once an El Nino is in full swing, and the ocean and atmosphere are well coupled. In that case there would be a longer period of steadier westerly wind anomalies due to the El Nino SST pattern, with wind blowing toward the location of maximum SST anomaly, typically in the Nino3 or Nino3.4 region, or even farther west over the dateline (as is the case in the current weak El Nino).