"Does checking/unchecking the Total Distribution Checkbox change tax liability?"
Generally, no. However, if it's a distribution that can at the option of the recipient be taxed differently if the distribution is a lump-sum distribution, box 2b Total Distribution being unmarked would imply that the distribution is not a lump sum distribution. Examples that require a lump-sum distribution are distributions from an employer plan of Net Unrealized Appreciation of company stock and special 10-year averaging of distributions from employer plans for those born before January 2, 1936 and their beneficiaries. Doing any of these options within TurboTax would require more than simply marking the Total Distribution checkbox.
The full list if items requiring lump-sum distributions is here: https://www.irs.gov/taxtopics/tc412
"Does checking/unchecking the Total Distribution Checkbox change tax liability?"
Generally, no. However, if it's a distribution that can at the option of the recipient be taxed differently if the distribution is a lump-sum distribution, box 2b Total Distribution being unmarked would imply that the distribution is not a lump sum distribution. Examples that require a lump-sum distribution are distributions from an employer plan of Net Unrealized Appreciation of company stock and special 10-year averaging of distributions from employer plans for those born before January 2, 1936 and their beneficiaries. Doing any of these options within TurboTax would require more than simply marking the Total Distribution checkbox.
The full list if items requiring lump-sum distributions is here: https://www.irs.gov/taxtopics/tc412