(Without knowing how old you are) The honest answer is no, but it's a perfectly reasonable starting point. At least it proves you aren't Jabba the Hutt! If you aren't doing them already, I would suggest substituting a session of hill sprints into your training programme every so often. This will have the effect of toning up all the muscles you need for running, and much more quickly than just normal distance running alone. It should also help you improve your running form (i.e. your posture and stride length), because sprinting means you are naturally striding out further than when doing normal distance running. Forcing your body to become accustomed to a longer stride length than normal will tone up the corresponding muscle groups, and make it easier for you to stride out when doing your normal distance runs. Before you know it you will be running quite a bit faster, just because your body is working more efficiently.
First find yourself a hill/long slope. A track or off road is better than tarmac/concrete for your body's wear and tear! Use trees, lamp-posts or whatever as markers, and select your starting point. Now start by running up the hill at what is for you a fast comfortable running pace. This should be a touch faster than the fastest you could run continuously over a distance of say two miles. At some point going up the hill you will either be too out of breath to go on, or your legs will turn to jelly. (Actually, this will also give you a good indication of whether it is your aerobic circulation or your muscular endurance which is letting you down.) Stop where you are, and make a note of how far up you are. Pick a point one-quarter of the way up from where you started. That first quarter is going to be your first 'target' for your hill sprints. Walk back down to the bottom, and when you are ready, run flat out up to your target. Whatever you do, don't stop, and try not to slow down. Now walk back down, rest until you are ready and do it again. After a few reps you will find you are running much slower. That tells you how many reps you should be doing as your starting reps. Don't worry if it is only two at first - you will soon be able to build up.
Over time you should find that you are able to increase the number of reps you can do, and decrease the time you rest between reps. When you can do six reps with not more than one minute rest in between each, move your target point a bit further up the hill. You will find you can't do as many reps, but again build it up until you can do six.
I would suggest that when you first start doing hill sprints you shouldn't do them more often than every third day. It will take a week or two for the muscles in your legs to build up to the point where they are strong enough to support your joints from the unfamiliar stresses and impact shock. Once you are comfortable (and you will know when that is) you could occasionally do them with just one day's rest in between.
On press-ups, you have two minutes to do as many correctly executed press-ups as possible, and you may rest at any time during the exercise and then continue. By all means do progress tests like this every so often, but just doing this test all the time isn't the best way to build up your score.
I have always found that the real cutting-edge Combat Engineers to be some of the fittest (and bravest) chaps going. If that's what you really want, make sure it is what you are thinking about when you are doing PT. Your body will do whatever you want it to do, if in your mind you want it bad enough!