No the beat error is nothing to do with the mainspring. It is caused by the impulse jewel being rotated/misaligned relative its correct “at rest position”.. When the balance is in the watch on its own (no pallet fork), the impulse jewel should sit in between the banking pins. It is analogous to a pendulum clock being out of beat. In modern watches the beat error is easy to correct but in old watches it is not and adjustments have the potential to wreck the hairspring. On an old watch the hairspring collet has to be rotated to the correct position on the balance stuff. On a modern watch a two-piece regulator allows the hairspring securing stud in the balance cock to be rotated like the regulator. Read up about this and for what it’s worth, I’d leave the watch with a significant beat error unless you are skilled and confident to correct it.
See this video for an explanation: