It's worth saving - investing (I assume you mean in the stock market/index/mutual fund) probably wouldn't yield very significant growth but it is worth saving what you can.
Investing accidently helped me save. If I have money in an account, and I need to use it, I will, but by buying stocks and bitcoin, I don't have that money, I have things that will increase in value that I can sell for money. And there have been a few desperate times that I had to do that, but my brain is far more unlikely to take a hypothetical future loss, than spend all my money today.
Truth. Lots of money to be made in crypto but it's basically gambling outside of eth and BTC. I make decent returns playing with memecoins but you have to watch it for awhile and know when to sell/buy etc... for example, now it's a good time to throw money into Shiba Inu coin. It's down a lot, which is normal, but it'll go back to higher numbers soon, as it always does. Once you get a feel for what a normal low and high are you can just set auto buy/sell at those points and make decent profits.
Of course, when it comes to crypto, Bitcoin and eth are more like commodities and are generally safe. Shit coins are high risk but but $50 in a shit coin could be $150 overnight if you know what to look for.
Edit - don't fuck with big money in crypto unless you're willing to lose it, but $10 here and there can be fun and often profitable.
Why would the absolute amount of money matter for investing vs. saving cash? Assuming he finds a broker for which absolute transaction fees are negligible, the only important factors should be time window and risk tolerance, both of which are independent of the absolute saving rate.