Not necessarily. In Tezos you can actually delegate any amount of coins and participate in the staking process - simply by delegating your Tez to a baking service. Yes, in Bitcoin there's mining, in Tezos there's baking. It doesn't matter if you own 10, 100, 1000 or any other amount of tokens.
If you own a roll, which is 10k XTZ, you can bake on your own. This requires you to be online 24/7 on dedicated hardware. However, it does not require energy-intense mining rigs -- in fact all it takes is low-end hardware, even an older laptop is enough. This is enabled by an elegant system called Liquid Proof of Stake.