If you're going to meet with someone, be sure that you can commit to being mentally present. It's easy to delude yourself into thinking that you can multitask sending / reading a few emails. But no matter how good you are at multitasking, the fact that you're doing it dramatically changes the nature of your conversation. No one is that slick.
People know when your mind is elsewhere. So, if you can't afford to the time, be upfront and reschedule the meeting. It's more respectful of both of your time. Not only will this give you a chance to stop feeling behind, but it'll also prevent you from making the person you're meeting with feel slighted.
While I believe in the Woody Allen adage, "80% of success is just showing up," it only counts if you're there both mentally and physically.