What are the consequences of not keeping Sarissa's secret?

If you decide to reveal the secret, you will get another decision allowing you to replace her with Vederia, or to support her continuing to serve as the Asari pathfinder. So, we're dealing with three possibilities here: keep the secret, reveal the secret but keep Sarissa, or reveal the secret and choose Vederia as pathfinder:

Don't Reveal

Kalina has reported on what happens if you keep the secret:

If you choose to keep the secret you'll still confront Sarissa so she'll know that you know but she is now under the understanding that you're keeping the secret for the greater good and to keep hope alive. Cora will have many conversations with you about the decision and depending on the choices made gets over it and moves on. With this choice Sarissa turns up during the final priority mission to provide additional fire support during the main push.

Reveal and Keep Sarissa

This is what I did on my only playthrough so far.

This resulted in a significant amount of dialog with Cora, not only on the Asari ark but in further conversations aboard the Tempest and in Pathfinder HQ. Cora was conflicted about the decision, but not angry with me. Based on Kalina's description, it sounds like, although the exact words might change, this is basically the same as keeping the secret.

Sarissa can be found in Pathfinder HQ.

l I indicates that she will show up in the final mission.

Reveal and Choose Vederia

According to Polygon,

Your decision only effects which asari shows up to help you during the end of the game.

Which implies that if you choose Vederia she will show up to aid you in the final mission. It also corroborates our two user reports indicating that Sarissa aids you in the final mission in both the other options.