To say that is a stretch is an understatement.
I'll explain why it sounds preposterous to me, and why the idea that google could change the fate of cancer research or missions to mars if not for its profit motives is patently unrealistic to the point of being insulting to everyone involved in this counterfactual.
1. Why cancer?
Number one cause of death is heart disease. Why not that? Surely the #1 problem is good enough for people currently working on adtech if the #2 problem is.
You said curing cancer, not "applying the numerical optimization expertise of a tiny fraction of google's workforce to the occasional omics problem in collaboration with a research lab" or "headhunting the PI of a lifesci research program to build an initiative at Google" or "throwing google infra at something other than Stadia". Even something far more obvious like "applying deep learning to diagnostics / early detection / etc."
These are the things Google can actually do, and they are the things Google already does. Examples: DeepMind for breast cancer screenings, Public Datasets program support for selected research. Still no cancer cure. So if you'd said that, well, they're doing it, to whatever extent they deem worth the prestige bump.
Unless they decide to become Microsoft and buy out entire sectors of applied biotech, they're not going to radically improve their hands-on involvement in lifesci relative to what they're already doing.
More, just ballpark the numbers. Google has 100k employees — "98771" in 2018-12 as per their SERP infobox. "A lot" of those employees absolutely do not by any stretch of the imagination possess the skillsets required to assist in meaningful ways on high-end cancer research, unless that work is conducted like some kind of wartime effort and the assistance is largely of a clerical nature.
And in the event that Google employees were being unilaterally drafted into this effort as grunts, the very first thing they'd do would be to crowdsource/outsource the bulk of the menial work to cheaper labor sources beyond Google. So their main contribution would undoubtedly be in building the scaffolding required to pass the buck.
2. Why Mars?
This constitutes a complete diversion of Google's autonomous driving and robotics people to an out of the blue project that they're out of position to handle. It would merely sabotage a division where Google is a market leader for the sake of starting up an incoherent, laggard mess in an area defined by maddening bottlenecks and complexity. Google has no substantial preexisting expertise in this area, afaik.
At one point they put up 30M USD in sponsorship prize money for a lunar lander competition, but that's about all that comes to mind. It also went pretty dismally. They had to repeatedly extend the deadline. Eventually the comp ran 11 years and ended in one launch -> one crash on the lunar surface. They threw a mil at the team as a consolation prize.
That project was more of an exercise in reifying the moonshot metaphor than anything else.
One far more recent indicator of how hard it is to make strides in this area is the DARPA Launch Challenge, intended to accelerate radical improvements to launch pipelines. It just closed without a winner. One team barely made it to the launchpad then scrubbed.
In terms of both social good that Google can do with its nearest preexisting R&D and profitability, it's clear that redirection would be disastrous. Autonomous vehicles are the play for them. This has nothing to do with the adtech people either way.
All in all, the relevance of Google to either of these problem areas is about what would be expected, cet par: not a lot. Modern work with any technical bent is hyper-specialized. There's no jump from literal cancer like adtech to actual cancer.
On top of that, adtech is largely a house of cards. You can't ever assume that 'data science' coupled to business requirements and marketing is in any way rigorous or indicative of the current state of the art in independent research. A lot of this work is pure smoke and mirrors operating on greater fool theory. To specialize in that sector is to specialize in window-dressing falsity. So it's not like you'd want adtech data jockeys touching subject matter that actually matters.