I think this is what you are looking for -
select Address1+Address2 as CompleteAddress from YourTable
where Address1+Address2 like '%YourSearchString%'
To prevent a compound word being created when we append address1 with address2, you can use this -
select Address1 + ' ' + Address2 as CompleteAddress from YourTable
where Address1 + ' ' + Address2 like '%YourSearchString%'
So, '123 Center St' and 'Apt 3B' will not be '123 Center StApt 3B' but will be '123 Center St Apt 3B'.