Yes, that at any rate. However, don't confuse transaction blocks with multiple exclusion blocks. A transaction, by itself, doesn't preclude concurrent users/processes from reading and updating the same data. The potential for conflict arises only through concurrent updates.
The race condition in your unadorned code results from a difference between time of check (state == x) and time of change (state = ...). There are two strategies to avoid the resulting inconsistencies:
Optimistic locking, as Fred indicated in another reply. With optimistic locking, you run headlong into the race condition, but when writing to the database you ensure that it can only succeed if is based on consistent data. On updating a record, ActiveRecord checks that the updated_at timestamp of the record as currently stored is the same as the timestamp when the object was read. An identical timestamp indicates that there haven't been any intervening updates.
Pessimistic locking is another way. You can either #lock! an object you already have or #find(..., :lock => true) get a locked object to begin with. Locking an object like this precludes any changes to the corresponding database row until the locking transaction is either committed or rolled back.
Rails gives you optimistic locking automatically for tables that have the requisite timestamp columns (updated_at). Pessimistic locking you have to do explicitly. As a guess, I'd say that pessimistic locking is only worth your and the database's effort if conflicts are likely.
At any rate, with both locking strategies you have to take into account the possibility of a conflict. With optimistic locking, you get an ActiveRecord::StaleObjectError exception in that case. I'm not sure about pessimistic locking, but I guess you'll get an indistinctive ActiveRecord::StatementInvalid exception.
Michael