For a successful SaaS you certainly want to get awareness and...

For a successful SaaS you certainly want to get awareness and attention.
This seems to indicate that the marketing to attract users is working - so a big tick to the marketing team.
The next success comes if the platform actually does what it says it will do - that would be measured by usage and/or drop offs and relates to the efforts of the developer teams, user interface designers and architects.
if people continue to use it and income becomes surplus to outgoings, then we know the business model is working which is the efforts of the business strategist.
And then it's a question of handling growth, which relates to scaleability (for all those teams involved), and competition or changes to the market.

In my experience each team is important, but I have to say marketing and getting folks to download your app is by far the biggest hurdle.

The share price always reflects perception rather than reality. There are several unknowns that introduce risk to these models, however having a successful launch, getting market traction, are all good indicators. The more indicators that are proven or exceeded, the better the share price will become as an indicator of future sales. But there is a lot happening in the US at the moment and anything could happen.