Would using an albuterol inhaler cause you to become depend on it, and thus weak without it?

Albuterol. To my knowledge, there is no tolerance issues with albuterol. Patients with asthma use it in emergencies so there is an obvious attachment to it. If you find you are needing more then you thought you would, then you should probably get check out by a lung specialist to assess for moderate to severe asthma.
Different problem. If you find you are using it more often than 2-3 times a week, your asthma treatment plan is inadequate. You need to consult with your doc about a daily med that would get you into better baseline control. Using it as a single med, but using it often means your asthma is in poor control, not that the med doesn't work.