There is a minimum weight you must use to create a training stimulus, but yes, you can increase your 1RM with higher-rep sets (again, to a limit, they can't be sets of 100, the weight is too light).

To increase your 1RM at the most optimal pace, yes you need to specifically train the movement so that you can benefit from improved technique and neurological adaptation. But if I do tricep, pec, and front delt isolation exercises at higher reps, to failure, and see significant hypertrophy in these muscles, my bench press will be stronger, other things constant.