Good Afternoon, Justine,
This is an excellent question. There is no documentation regarding SEO benefits from the presence of thumbs-up activity on Google reviews. They may have some impact on the order in which reviews are displayed, but I have never seen any study undertaken as to whether they have any impacts beyond that.
Because of this, I would treat the topic, in general, as one of low priority/low concern.
However, we've waded into something deeper here with this scenario of a client trying to pressure an agency to thumb up his positive reviews. I'm assuming he's doing so because he believes it will benefit him in some way, but your question deserves a thoughtful answer.
So far as I know, Google has never released formal guidelines for the use of the "like" function on reviews since they rolled it out in 2016. They don't specify who should use that function (owners, the public, etc.) or whether they would consider any particular use of it spammy. But what we do know is this: Google is very big on the concept of reviews being honest and transparent and sourced directly from customers. Anything that resembles manipulation is forbidden.
The "like" button isn't the review, of course, but it's associated with the review. Does it strike you that what this client is asking you do is to manipulate his review corpus? After all, you are his marketer ... not a customer. Google's position is weak here, because so far as I know, they haven't released specific guidelines. In that environment, I could certainly make a case for your client interpreting the "like" button as something he should use when he receives a review he's grateful for. He could respond to the review and hit the "like" button as a thank-you. But when the owner begins bringing in his marketers to do the same ... marketers who are not customers but are, in fact, paid contractors, does this not seem to be crossing a line from gratitude to manipulation?
Another way to look at this: how would the business owner feel if his competitor hired 100 people who did nothing all day but like his reviews? Would that feel fair or honest to him?
So, as I said at the outset, I would consider this a low-level priority given that I have no documentation indicating that likes impact rankings, and I can't even fully quantify the level of impact they have on review ordering because you will commonly see reviews with multiple likes being outranked by reviews with no likes. This isn't the biggest issue in local SEO, but your client's attitude could prove troubling if he is inclined toward manipulation. I've never had a client try to order me to do something, and that that seems odd, too.
If it were my agency, I would say "no" and talk with the client about the need to earn his reputation rather than try to fake it in any way. That kind of approach seldom pays off in the long run, and I'd hate to okay a client engaging in any practice that I was even remotely worried might be perceived by Google as spam. You'll need to make a decision on this at your agency, and then present it to the client. Good luck, and I hope my thoughts on this are helpful!