Probably not, but you can try.
But first things first, I'd really recommend a 118mm ES71 for that setup. I'm not saying for sure the 113 isn't going to work, but I've had some trouble with those in the past due to the wide shell.
Just out of curiousity, what size seat tube / derailleur clamp does that bike take?
By installing a 68x113 into a 73mm shell, you're going to end up with your chainrings stuck out an extra 2.5mm -- essentially what you'd have with a 118mm spindle.
But on the other side of things (the non-drive side), that crank arm is going to be sucked in an extra 2.5mm.
Not only will that result in a net 5mm imbalance to your Q-factor, but you may find your non-drive crank arm is pulled into the bottom bracket adapter, preventing the crank from spinning freely.
If you're adventerous, and don't think you'd mind the 5mm imbalance much, give it a shot. But I'd really recommend a 73x118mm ES-71 for that bike, especially if you have a 34.9mm (1-3/8") seat tube/derailleur clamp diameter.