I think it would be a mistake to suggest a direct connection between that policy and the Revolution per se, but it was a reflection of the policy priorities of the Ceaușescu regime which created the conditions that led to its ultimate downfall, if that makes sense. I think the argument for an explicit connection between the abortion ban and the violent revolution originated with Freakonomics, which is really a case where correlation is misinterpreted as causation. Yes, Romania's abortion ban was unique, but so were other aspects of Ceaușescu's policy (e.g. extreme economic austerity in the 1980s and the largest and most repressive secret police apparatus in the Eastern Bloc) that have a much more obvious tendency to precipitate a violent revolution. That said, the abortion ban is a good entrée to looking at Ceaușescu's uh, unique brand of communist ideology.

Ceaușescu's ideology of "national communism" was, in theory, focused on strengthening Romania as a nation while also continuing on the path toward communism. Ceaușescu implemented policies (including the abortion ban and rewards for mothers who had large amounts of children) that were focused on increasing the population of Romania in order to increase its productive capacity with the assumption that this (along with paying off Romania's national debt) would enable it to essentially achieve economic autarky; this idea was influenced in some respects by Kim Il-Sung's Juche ideology (which Ceaușescu observed first-hand during a state visit to North Korea in 1971). The idea that a country of Romania's size was going to achieve autarky was completely ridiculous, but that was Ceaușescu's vision.

In practice, this obviously didn't work out as planned. The abortion ban itself mostly resulted in large numbers of unwanted and abandoned children who either ended up on the streets or in the infamous orphanages, as well as women circumventing the ban and obtaining back-alley abortions (as was famously depicted in Cristian Mungiu's film 4 Months, 3 Weeks and 2 Days). The regime's natalist policies only got more extreme over time (eventually women were subjected to mandatory gynecological appointments to assess their reproductive capacity if they weren't having children), and the problems they created were only exacerbated by the country's increasingly dire economic state. Ceaușescu's aggressive spending in his attempts to modernize the Romanian economy in the 1970s led to the accumulation of a large national debt (approximately $10 billion in 1981 USD), and his conception of economic autarky required that Romania pay off this debt, which he was determined to do by the end of the 1980s. He attempted to do this by imposing drastic austerity policies in Romania, greatly limiting the availability of even basic consumer goods (and therefore leading to substantial price increases even as real wages dropped), so that Romania could increase its exports and obtain hard currency to pay off the debt. The country succeeded in paying off its entire debt by 1989, but the effects on the Romanian population were dire, and the standard of living was lower for most Romanians than it had been a decade before.

This domestic economic crisis was accompanied by an increase in political repression in response to increasing popular discontent. Romania's secret police force, the Securitate, was the largest (relative to population size) in the Eastern Bloc, and arguably the most repressive. Ceaușescu was the last true hardliner in the Eastern Bloc, refusing to allow even a modicum of political liberalization like other communist countries (e.g. Poland and Hungary) did during the 1980s, and the repressive actions of the Securitate were essential for his ability to maintain political power as he grew ever more unpopular. Romania entered a kind of cycle of domestic unrest and harsh repression that became more frequent during the late 1980s. This process continued until something snapped, and the popular opposition to Ceaușescu eventually boiled over in Timișoara in December 1989, leading to uprisings in other Romanian cities and eventually the dramatic, televised revolt in Bucharest that signaled the end of Ceaușescu's regime.

So hopefully this additional context helps explain both how the abortion ban fit within the overall policy program of Ceaușescu's Romania and how those policies eventually fomented a violent revolution. The link is definitely more indirect than direct, but it's possible to understand how these events were interrelated if you consider the larger political and social context.

Sources:

Dennis Deletant, Romania under Communism: Paradox and Degeneration (Routledge, 2018)

Stephen D. Roper, Romania: The Unfinished Revolution (Routledge, 2000)

Vladimir Tismaneanu, Stalinism for All Seasons: A Political History of Romanian Communism (U of California Press, 2003)