Clearly, causality is difficult to determine here as we can’t have a counterfactual world with no ACA. At the same time, a paper by Buntin and Graves (2020) makes the case the suggestive evidence indicates that the answer is ‘yes’.
…[health] expenditures now account for 17.7 percent of the nation’s gross domestic product, compared to 17.4 percent in 2010.6 Despite the increase in overall expenditures, the annual expenditure growth rates in the years following the ACA’s implementation were generally lower than in the years before the ACA: Average annual national health spending grew 4.3 percent in 2010–18, compared to 6.9 percent in 2000–09…On a per capita basis, spending grew by only 3.6 percent in 2010–18.
ACA did expand health insurance coverage so we would expect a large jump in expenditures. However, ACA also aimed to decelerate Medicare spending through reduced reimbursement and more value-based payment (i.e., alternative payment models). Which effect was larger?
The Congressional Budget Office estimated the direct effects of these changes… and it found that the on-budget costs of greater coverage were larger than the payment-related savings in Medicare—although not by much per year in the context of overall health spending
As Presidential Candidate Biden was a major supporter of the ACA, one could expect this type of trend to generally continue (i.e., modest coverage expansions and some reductions in provider reimbursement) if he were to be elected.