The fact you made the first approach means they know you're reasonably open to changing jobs, but it doesn't let them conclude you're willing to take a loss on the change. It's entirely appropriate for you to work out what "taking a loss" means, for you.
So, provided you present your current arrangement as part of the overall salary/benefit package that they have to beat in order for you to take their job, then it's part of your leverage. Provided they believe that they need to beat your current package, and that this is part of your current package, it remains in play. The fact you applied for the job doesn't change that.
The employer might try to brush off cost of commute/relocation as insignificant, since it is after all your responsibility to get to work. You have to make sure they understand that you're still taking it into account when deciding whether to accept their offer. If there's nothing wrong with your current job then it's their responsibility to make a better offer if they want you to leave it. The fact you applied to them doesn't change that.
If you're desperate to change jobs, and they know it, then that does affect your leverage since they know you're willing to take a loss. Simply applying for a job doesn't let them conclude you're desperate, but if you've given that impression by some other means then you might be in trouble because of that.
Note of course that having any amount of "leverage" is only worth so much. You can't coerce the employer into hiring you, so like Joe says it won't get you above the ceiling they're willing to pay for the role. Leverage just means they won't waste time haggling below what they believe you might accept. This might mean the result of having leverage is they don't offer you the job at all because they simply can't afford you. Use your leverage on someone with deeper pockets (or who has a more senior role you can fill). Let someone else have this job, who'll do it for what this company can afford.