I suppose anything is possible, & rods today may be made identical today, but I wouldn't be betting any money on it.
Back in my racing days neither Cosworth or Holbay forged rods, which cost about a months mechanics wage each did not come balanced, or even straight.
You can balance them yourself, if you like fiddly jobs. You have to support one end & weigh the other on a very fine scale. You can use a gudgeon pin across a couple of horizontal knife edges for the big end.
You will need a mandrill carefully machined to a neat fit in the big end to then weigh the little end. You need to get the whole rod, & each end to the same weight by the removal of metal.

Note, don't grind the whole rod away.
It is a time consuming & fiddly job sure to give you a head ache the first time you do it, but is not rocket science.
We machined up a longer mandrill to replace the gudgeon pin, & measured the rod for straight by checking the mandrills for parallel, & by using a fully true lathe bed we could check the thing for twist, by sitting it on the mandrills.
Is this all worth doing? My F2 Brabham finished every race it started in the 20 months I raced it, & I believe it was this attention to detail certainly adds to reliability, & it won it's class in all but it's first race, beating many F1s in the process, so I believe it is no determent to power development either.
Hasbeen
PS. Google balancing a conrod, & you will find both high & low tech methods.
Hasbeen