The ACA requires your insurance carrier to send you a statement showing the months you were covered. This was originally in the law because there was a financial penalty for not having insurance (the individual mandate and penalty). Congress changed the penalty to zero, but did not eliminate the reporting requirement for insurers.
As to tax implications, I don't know how the ACA is handled. Private insurance premiums are not considered part of your medical spending for federal taxes, but you should consult a tax expert about ACA insurance. If your state has an income tax, those rules may be different than the federal as well. My state has a lower threshold for medical cost deductions (2% of adjusted income) and allows insurance premiums to be included as medical expense if the premiums are paid with after-tax dollars.