It would, IF your debt / income ratio is currently above a percent and IF dropping said card would lower it below a certain threshold as illustrated in the below guide:

Financial Health Barometer
If your debt to income ratio is:

Less than 30%: Excellent!
30% to 36%: Good. You won't have any problem with lenders, but work to bring it down below 30%.
36% to 40%: Borderline. Some lenders will still give you a loan but you may struggle to make your payments.
40% or higher: Red flag. Your credit situation requires attention.

What helps further is pay down balances.