I have watch token accounts for various ERC-20 tokens within my Ethereum Wallet. Is it possible to send Eth to any of these token accounts within the wallet that would increase my token holdings within that watched token?
I think you have a misunderstanding of how tokens work.
Not only is a fee required (gas), but you almost certainly cannot simply send ether to the contract and increase your token holdings. Most token contracts have a 'sale period' which ends either due to a
time constraint or an
amount raised constraint. Once those limits are met, no more new tokens are 'sold.'
It's the same as a stock in a company. You can't just send a company money and tell them to give you an ownership share. You have to buy their stock on a market of some type.
Those markets are called token exchanges, and they are either an established 3rd-party exchange or some sort of decentralized peer-to-peer exchange. (I won't recommend any because I don't know which ones are good or bad.)
Some token contract will incorrectly accept your ether if you send it to them after the sale period, but that ether will almost certainly get stuck in the contract with no recourse to get it back.
For me it is not clear what you are asking.
Most tokens once the crowdsale is over no longer accept payments to create new tokens. If you want to increase the token balance you have to purchase tokens through an exchange.
In the current version of the Ethereum blockchain any operation in the blockchain consume some gas and the user has to pay for it. A contract can simulate the user not having to pay for the gas by refunding the cost of the transaction, but someone have to fund the contract to do so.