If we don't want to use the conversion event code provided by Facebook Pixel, it definitely won't track the conversions.
But could not using it potentially result in higher ad costs (mainly bids) for future ads?
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Like Google, Facebook adjusts its ad prices on a "quality score" that includes click through rate as a major factor. Here is a site that explains it:
The click-through rate in itself is another factor that has impact on the Facebook ad prices. The higher CTR you can achieve, the greater chance you have of winning auctions.
In an auction, Facebook’s algorithm give a quality score to each ad taking part in the bidding and many argue the CTR is the most important factor to determine the score.