Yes, but you have to use more than just Tendermint. Tendermint itself is a consensus engine that doesn't know anything about application states or virtual machines. All it knows is that it needs to order transactions, which are just arbitrary bytes. To make Tendermint useful, it can relay transactions to an application running in another processes, using TMSP, and that application can be written in any language and support any arbitrary application state. So you can take existing ethereum codebases, adapt them to TMSP, and run them with Tendermint instead of ethereum's proof of work. And you can do this for the implementation in every language!
In fact, we've already done this in go:
geth-tmsp is a fork of
go-ethereum that satisfies the TMSP interface, so it can be driven by a Tendermint blockchain. That is, you can use existing go-ethereum tools and web3 like you would, but with a Tendermint backend instead of the Ethereum networking and proof of work.
eris-db is a smart-contract blockchain that hosts a fully compatible EVM (ie. you can run solidity contracts), as well as a capabilities system and a global key-value store. It also satisfies the TMSP interface and is natively driven by Tendermint.
We are working towards the launch of a public blockchain called Atom, which is really just a generalization of sidechains using Tendermint. One of the sidechains will host the EVM, so there will be a public Tendermint-powered blockchain hosting the EVM.