Regarding your question whether the needles will have to be leaner or richer, the answer is "it depends". During combustion, a fair amount of conventional oils burn but with synthetics, some oils don't burn at all where others burn more like conventional oils. If the synthetic you choose doesn't burn in combustion the needles would have to be a bit richer. Likewise it the oil burns a bit, the needles may not change at all or may have to be a bit leaner. A ratio change will have more effect on mixture than changing types of oil.

The point that others have made is the main one. Just tune the engine as needed. Likely you won't have to move the needles more than a blade width one way or the other. A friend just made the switch from Pennzoil to Red Line and the only needle changes were about a blade width leaner on the low needle.