Which problems can be expected by continuing to use a MacBook Pro Battery already due for replacement?
I use a similar model of MacBook Pro (15” Late 2013).

The batteries have something called charge cycle (1 charge cycle = 1 full charge and discharge). The MacBook Pro battery typically retain 80% charge holding capacity after completing 1000 cycles.

Although the advanced lithium-ion batteries in MacBook is meant to last for several years before they begin to lose their overall charge capacity, there will eventually be a time when it will need replacement.

This is reported by macOS by alerting you about battery condition. You can also view the current cycle count of the battery by going to Apple Menu → About This Mac → System Report... → Hardware → Power → Battery Information: → Health Information: → Cycle Count.

There are also various 3rd party apps which you can use to determine the current battery health status. coconutBattery is one such popular tool.

Once you are convinced that the battery need replacement, it is strongly advised to do so.

Also, the top case, keyboard, trackpad and the battery comprise of a single unit in the MacBook model you own. The entire unit will need replacement. (I got mine replaced a few months ago). That explains the hefty price tag.


  Which problems can be expected by continuing to use a MacBook Pro Battery already due for replacement?


Continuing to neglect replacement may end up damaging other components thereby leading to more expenses. In my case (pun intended :-D), the battery started swelling which could have also ended up damaging the logic board assembly.

Other obvious issues include, lesser backup than expected, random shutdown under load and possibility of reduced performance at times.

If you haven't done so in the last 5 years since you bought the MacBook and macOS is alerting you about it, it's highly recommended to get the battery replaced for extending the lifetime of your MacBook Pro.