The Premier League has a large number of imports, with 390 the current approximate figure. Every Premiership squad has some foreign players. So, the answer to whether a quota would make any difference in the Premier League may seem obvious.
Leagues That Have Notable Foreign Player Restrictions
Argentina restricts its clubs to signing only six foreign players. The Primera División restricts foreign player selection to five foreign players in a squad for its league games. That’s a notable restriction that has seemingly helped the Argentina soccer team, the current world champions.

Foreign player quotas in the top European soccer leagues are generally far less restrictive. The French Ligue 1 restricts non-EU foreigners in squads to four. There’s an exception made for African players in French soccer. A maximum of four non-EU players in Ligue 1 squads is still a somewhat bigger restriction on foreign players than what the Premier League currently has in place. The Premiership permits a maximum of 17 non-homegrown players per squad.
What Could a Premiership Foreign Player Quota Be Like?
The strictness of a potential Premiership foreign quota is important to consider. That is to say, how many foreign players a Premiership squad would be allowed to have in its matches. Let us say the quota was six outfield players and 12 foreign squad players for matches. Note that Premiership clubs can select 20 players for Premier League matches with nine on the bench for substitutions.
The bigger clubs generally tend to have more foreign players. Manchester Utd have many foreign players in their squad at the moment, 19 out of 26. Their matchday lineups would certainly be adversely affected by the quota restriction of 12 foreign squad players.

A restriction of 12 foreign squad players would give the Premiership scope for 240 imports. That would be less than the current figure of 390. Overall, the hypothetical quota stated would amount to approximately half an average squad of 24 players.
Alternatively, let us suppose it was a restriction more like four foreign outfield players and eight squad players. That would seem quite restricting, and the impact it could have might be felt by many teams within the league. That would cut the number to 160 foreign imports, which is a lot less.
The Potential Impact of a Premiership Foreign Player Quota
The larger clubs would undoubtedly feel it. Man Utd, again, would have to leave some of their first-team foreign players on the bench and rotate. Increased demand for UK players would probably push the prices of top British players up.

At any rate, smaller clubs would struggle to acquire the best British players on the market and would likely rely more on their youth setups than ever. No doubt, the smaller clubs would fill quotas to the maximum and then field younger English players.
How positive such a foreign player quota restriction would be is open to debate. More English players on the pitch, instead of the bench, would probably be a welcome sight for most. However, equally, such a lack of choice will not help the smaller clubs, and higher prices for English players will ultimately create financial difficulties.

The best English players from the top Premiership youth academies are going to be playing for their clubs to begin with. Premiership clubs could sell them for bigger fees. Meanwhile, any talents from the smaller clubs will be more important to keep hold of, given the quota, as opposed to selling.
At any rate, a quota would reduce the number of foreign players in the Premiership regardless. Some of the best players, from Haaland to Salah, are imports. With a quota, the best of them would likely remain in the Premiership, but some decent imports would still be lost, along with some lesser players. The best of English plays in England, and that, of course, would not change.
End of My Premiership Foreign Player Quota Rant
So, I feel the answer depends on the severity of the quota. A light quota restriction of eight outfield and 16 foreign squad players for matches might not make a significant difference to the overall current number of foreigners in the Premier League. While those teams that field a lot of imports might feel it, most might not. If it were a more severe quota, as with the example given, it would make a difference because there would be far fewer foreign players. Yet, how beneficial such a quota would be for English soccer generally is still debatable.