Achievement: it is efficient, and avoids too much time on the phone. Instead of calling fifty people, each of whom requires at least 5-10 minutes of hello, goodbye, catch-up, pleasantries, etc., you can fire off a couple of messages a minute (assuming you type quickly!). Having a lot in your mailbox, however, may make the goal of cleaning out the email box unmanageably large and anxiety-provoking. If you can manage yourself long enough to do it, however, that can be very satisfying!
Affiliation: Could arouse concern regarding missing people--a classic affiliative concern, creating conflict unintentionally--or failing to respond rapidly enough; but also allows you to "touch" a whole bunch of people, reassuring people on your good intentions and yourself on affiliative anxiety...unless, as I do, I have to suddenly deal with a bunch of possible business trips which take me away from home, in which case you can get that affiliative clench as you anticipate half a dozen separations at once!
Influence: Whoops! Did you miss responding to your boss? Oh, no! How about a client or customer? Will you look like a slacker because you've taken off a whole week? (I once took off a week from Wednesday to Wednesday, so I had part of each of the weeks to work!) Fortunately, again speed plays in your favor, but having a pile of responses does not. It might also be tempting to respond to everyone quickly to have a big impact right away--but if you don't read carefully you might not respond appropriately. This is a case where your motive could get you into a vicious cycle: I want to have impact, so I send out a flurry of emails, which makes me look careless and comes back to bite me, which makes me influence-anxious.
So what to do? Well, email can certainly make it easier to satisfy a motive, but you still have to manage the immediate impact. Here are some thoughts:
1. If 116 emails seem too much, find ways to "chunk" it down. For example, I get emails every day saying who is in the office--I can sort those and dump them immediately, thus eliminating five in about five seconds. Go through sorts like this enough, and pretty soon you have a more manageable number. Prioritize--I prioritize in four ways: urgency, importance, time required to answer, and time zone. I try to respond to time-sensitive questions immediately, address quick-and-important issues next, short answers next thereafter, and since I do international work, I try to respond to European questions before 10-11am (4-5pm Central Europe time) and push aside Australian or Asian questions, since people are asleep anyhow. What I am really doing is sorting it out by the level of anxiety they provoke! "Importance" may actually translate into "my boss's email, regardless of real importance."
2. Is responding within three hours your first day back any less impressive than responding within one hour? Pace yourself.
Especially given the time-zone issue. If someone isn't going to get your email for twelve hours, it earns you no additional points to have it done thirty minutes earlier. Take a deep breath, save some responses for the afternoon.
3. If you feel yourself spiraling out of control, force yourself to take a short break from email. Stand up, check your snail mail, chat with people about your vacation. You don't need to spend a lot of time on this--just enough to break that obsessional, anxious rut you can get into when addressing a lot of small things in a row. Five minutes can be enough to reset your head, and tackle it again.
4. As you get anxious, take a second to check how many emails you have left--and think of the progress you have made! I went from 116 down to 26 in the first hour and a half I was in the office, and when I realized that, I quit panicking. If I can do 90 emails in 90 minutes, clearly I am going to catch up!