Anger and outrage are valuable, and it's important that we channel them in the right directions.
It might very well be, and it's worth debating how much giving business support to an organization whose policies you (possibly vehemently) disagree with is a kind of implicit support of those policies. But, it's also worth asking: if protest by workers to put pressure on their employees to stop giving business support to organizations whose policies they vehemently disagree with is "disappointing," what kind of protest isn't?
It seems to me that when we're talking about corporations, who you do and don't sign contracts with -- who you buy from, who you sell to, and what charities you support -- is far and away the strongest signal you can send. If you're sending a signal of support to Black Lives Matter protests, it's nice if you send out a few tweets and update your home page, but it's better if you donate money, services, and/or employee time. And the group you donate those things to is going to send a signal: donating to Colin Kaepernick's "Know Your Rights Camp" is in some sense a more specific, stronger message than donating to the ACLU.
So it certainly seems reasonable that asking the corporations you work for (and perhaps work with) to put their money where their PR is in terms of who they do business with also sends a message. No, it's probably not in and of itself going to put much pressure on ICE, but it is a statement of values.
It's important to channel them in all directions that could have impact. You never know for sure which 'direction' matters to the group you are trying to impart change on.
In this case, GitHub took actions similar to what you describe, donating $500k to "nonprofits helping communities adversely affected by the Trump administration’s immigration policies": https://www.latimes.com/business/technology/story/2019-10-31...
Personally I think $500k is a bit small, and if I were Nat Friedman in this situation, maybe I would have announced a few extra paid leave days for employees engaging in protest, strikes, visiting elected officials to lobby for change, etc.
Nat Friedman's quote on this particular request from employees is "Picking and choosing customers is not the approach that we take to these types of questions when it comes to influencing government policy."
Even if there is no direct impact (such as another supplier stepping in) an individual choosing to avoid directly, supporting an organization they cannot morally abide has personal moral value. Probably not in a utilitarian sense, but that isn't the only basis for moral action in humans - see the trolly-problem for the canonical example.
[I bet I'll get more downvotes than answers].