Not without Push the Limit. Han Solo's action should be evade every turn. Frankly Han Solo + Gunner doesn't need more help hitting things.
Han Solo + Marksmanship + gunner.
I disagree. The Falcons ability to stay out of firing arcs and still shoot is what keeps it alive. I've seen many good players have to make a green maneuver because they used ptl and are stressed. They get blown to bits because their opponent knew exactly where they were going. The biggest down fall of stress on a ship is it limits the effectiveness of that piece.
As for the argument that Han's ability is good enough on his own, I think this is some what accurate. First in this game dice always favor the attacker. With that said a focus is a half hit. It is also an extra picture on the dice. Now when I'm looking at a 5/8 chance of rolling a picture on a dice and that's all I have to do, great! The problem when you rely on Han with a focus is that your average attack is two hits and this is easy enough for a Fel or any other tie to evade out of. Yes gunner will kick in and you will shoot again but did you spend a token? Did your opponent? Marksmanship changes ALL attacks made by a single ship. So both your gunner attack and your first attack are modified. Combine that with the reroll from Han and you should always be doing damage. This should also get you around the lucky roll of a tie fighter. This also burns your opponents tokens for your other fighters to attack.
Also marksmanship is changing a single focus roll to a crit. At range one this gives Han the ability to not only one shoot a tie fighter but an x-wing by landing a crit. (I've done this more then once.)
Let's also look at how an opponent gets around marksmanship, specifically a tie fighter, on a hit hit hit roll I'll take one damage by using tokens. Now if it is a hit hit crit roll and my opponent has a gunner to think about with a modified roll and he chooses to eat a crit well, Blinded pilot, direct hit, counsel fire, and injured pilot, are a few reasons why Han is better with a gunner and Marksmanship.
If we look at up coming meta we are looking at ships that deny a reroll and deny token use. In the next few weeks you will see a shift in meta to Marksmanship just to deal with Acion denying ties.