The full client (or the fat client) has to replay all the transactions on the state to ensure the validity.

What you are looking for is a variation of a light client which is being currently in research. The idea is to be watching only part of the state and use other peers for parts of the state that has less interest.

Yes it is possible you can connect to a remote node using web3.js

Adding web3

1. npm: $ npm install web3
2. bower: $ bower install web3
3. meteor: $meteor add ethereum:web3
4. vanilla: link the dist./web3.min.js

Then you need to create a web3 instance, setting a provider. To make sure you don't overwrite the already set provider when in mist, check first if the web3 is available:

if(typeof web3 !== 'undefined')
  web3 = new Web3(web3.currentProvider);
else
  // set the provider you want from Web3.providers
  web3 = new Web3(new Web3.providers.HttpProvider("http://localhost:8545"));

Create a Wallet Address

Install ETH-lightwallet

npm install ETH-lightwallet

sample code to create a wallet.

// generate a new BIP32 12-word seed 
var secretSeed = lightwallet.keystore.generateRandomSeed();

// the seed is stored encrypted by a user-defined password 
var password = prompt('Enter password for encryption', 'password');
lightwallet.keystore.deriveKeyFromPassword(password, function (err, pwDerivedKey) {

var ks = new lightwallet.keystore(secretSeed, pwDerivedKey);

// generate five new address/private key pairs 
// the corresponding private keys are also encrypted 
ks.generateNewAddress(pwDerivedKey, 5);
var addr = ks.getAddresses();

// Create a custom passwordProvider to prompt the user to enter their 
// password whenever the hooked web3 provider issues a sendTransaction 
// call. 
ks.passwordProvider = function (callback) {
  var pw = prompt("Please enter password", "Password");
  callback(null, pw);
};

// Now set ks as transaction_signer in the hooked web3 provider 
// and you can start using web3 using the keys/addresses in ks! 
});