Obviously, I don't have all the info but as a repair shop, I will say that it is indeed possible. Whether this is the case for you, I couldn't say.
An iPad mini is an older model at this point and if you never had the battery replaced it is logically much closer to the end of it's life than the beginning. Batteries degrade over time and we don't usually notice anything until it becomes painfully obvious. Also, depending on our usage and charging habits, you may not really notice a difference.
So what I would do right now is download either coconutBattery (Mac) or 3uTools (Windows) to see the battery condition. It will tell you what the percentage of the design capacity is left in the battery. Anything less that 75% will mean the battery is not holding a charge for very long and anything less than 60% means the battery is pretty much done.
Now, as an aside, whenever someone brings an iPad in for repair, I always test the battery first. iPads are secured with adhesive and are a major pita so I wouldn't want to have the customer (or me) open it again just to change a battery. Kinda like when the city re-paves your street and later in the year, some utility tears it up to change wires or plumbing or something...dumb and avoidable.
Another point to consider is that changing a cracked digitizer really doesn't require the tech to play around with either the battery or logic board so unless they had a serious brain cramp, it's hard to see how the two are related.