yes, the LT gains and LT distributions add to AGI, but they are not part of the calculation for ORDINARY tax bracket.... ST gains and ST distributions are part of the ORDINARY tax bracket calculation.
look at the schedule on page D-16 and if you want to go through the gory detail, as you state Line 1 is taxable income, but lines 2-43 decipher what is taxed at a capital gains rate, leaving line 44 as the part that is taxed as ordinary income; line 44 is taxed using the ORDINARY tax tables.
LT distributions and LT capital gains will have no impact on Line 44 as that are netted out during lines 2-43, so there is really no need to worry about these numbers in estimating where an IRA distribution trips you into the next tax bracket.
Trust me, I do this calculation multiple time during the year for exactly the same reason the questioner is asking.
https://www.irs.gov/pub/irs-pdf/i1040sd.pdf
