Yes it will. Try looking up a transfer station. They recycle battery’s there. I’ve done this before. And ask the attendance if you may look for a decent one that’s been recycled. Go in with a tester or as I proofer a piece of twelve volt wire if it’s hot it will burn that wire instantly. Try it.
Replacing the weak battery is not a problem short term. Connecting two batteries with different capacities in parallel is technically fine since the batteries will be operating at the same voltage. Charge and discharge current will be shared, based on capacity. It is best if the batteries are of the same type and age. For example, avoid combining a sealed (gel or absorbed glass mat) battery with a flooded (conventional) battery because they have different charging setpoints. Broadly speaking, you can parallel batteries without problems, and the charge controller will look after them. Just make sure you give them plenty of charge. If the system tends to operate at less than a full state of charge, adding new batteries to old will probably just result in the old ones pulling the new ones down and everything getting sulphated.
Assuming they are twelve volts, buy one and use only the new one, than buy another one next month and hook it up with the one you bought the previous month. If they are very weak and almost dead than DO NOT hook up the new one to the old one as the old one WILL draw the new one down to its level.