Say an S Corp has one owner and earns 300k in a year. It pays wages of 100k. Can the 200k be invested by the S Corp so that the the 200k does not have to be distributed?
Yes, but your use of the phrase "so that the the 200k does not have to be distributed" makes it seem like you're thinking distributions are mandatory, which isn't the case. Distributions are optional; nothing forces you to distribute the profits; you could leave the money in the company bank account if you wish or even "invest" in mutual funds or real estate.
Note the $200K profit would flow to the S-Corp owner as regular income, and income tax on that amount would be owed. Typically you would distribute enough to cover the tax owed, but you aren't required to. If you have enough personal funds to pay the tax without distributing it you can leave the entire $200K profit to reinvest in the company.
I'm going to assume that the $100K in wages is going to the owner too (because the owner should be taking a reasonable salary), in which case you would pay both sides of the FICA taxes on the $100K and income tax, whereas with the $200K profits only the income tax is owed whether you distribute it or not.
As a side note, your profits will actually be less than $200K, since you will certainly have deductions, one of which is at least 7.65% on the $100K for the employer portion of FICA.