It depends on what counts as "realistic." It was certainly an uphill battle.

Let's start with the good news for Perot. Early in the campaign, Perot polled very well. In June 1992, Gallup actually had him in the lead with 39% of the vote (vs. 31% for Bush and 25% for Clinton). That's a very strong showing, and Perot's final tally of 19% of the vote is impressive (though he got no electoral votes).

The bad news for Perot is that his path to victory was very narrow. In order to win the Electoral College, you need an absolute majority of electoral votes nationwide. Generally, you win a state's electoral votes by getting the most votes in that state (whether or not it's a majority) but getting the most electoral votes nationwide isn't good enough. If no one wins an absolute majority, then the election is decided by the House of Representatives.

Regardless of what happened in the presidential election, the House of Representatives was going to end up in the hands of either the Democrats or the Republicans (and very likely the Democrats given what was then a multi-decade winning streak). With votes splitting three ways, it's hard to get to an absolute majority, and this posed a real problem for Perot.

In fact, Perot dropped out of the 1992 race in July for this very reason, arguing that his continued candidacy would just send the election to the House (he likely had other motives as well). Shortly thereafter, he re-entered the race, but his support never again came anywhere close to the 39% share in June.

If Perot had kept 39% of the nationwide vote, he likely would have won the Electoral College. Exit polls showed that his support came about equally from voters who otherwise would have support each of the other candidates. Assuming that pattern held true, then Perot could have won an Electoral College majority with roughly 35% of the nationwide popular vote. Anything less, in the 25-35% range would have most likely sent the election into the House of Representatives.

So, could Perot have gotten 35% of the vote? It's possible -- after all, he did poll above that level in June -- but it's not very likely. Perot's peak popularity in the earlier summer came on the heels of two relatively bruising primary campaigns, and voters started migrating back to their "natural" homes before he dropped out. This was particularly true for Clinton, who had narrowly won in a crowded Democratic field but managed to rapidly win back disaffected Democrats after the Convention. By the time he dropped out, Perot's numbers had fallen to about 20% on the heels of multiple scandals and unforced errors.