My qualification for answering this
I am no fitness expert beside being involved in sports even before teen years. In my teens and early adult life i would train 4 to 6 days a week, until I started working. I am also a software developer, and been in industry for way more than an hand full so I can relate easily to you.
Yes. Anything is way better than nothing, although walking more, even around the office, while you stretch may be a better option. They may not make you lose weight but will improve you life quality, and may be enough for removing those pains you say your have.
First of all, lets step out of fitness, since neck and back pain may not be related to it. Sometimes you need to have a better chair or posture at work. We do sit a lot, even more than we are suppose to. There are even few offices that offer standing desk for their workers, I've already tried to implement that in my actual office. I can say it's a good experience, but I am sitting right now as everyone else.
Second, you say
we don't get a time for anything else
Although I know the felling, and almost everyone around me says that, believe me, most of times is untrue, and I would bet on 99,99% of the times. I know how a start up can be time consuming, or how a large corporation can be demanding, I had to travel or work at night due to time differences to customer, etc. Simply put, Software developing is demanding, and you pass most of the time sitting in a chair. When I started working my first full time developer job I went from super active to couch potato in a few weeks. I tried to exercise on week-end, but when I wasn't working I was trying to catch with my social or family life.
Don't have time, and wish to exercise more, make time then. Get up early in the morning, or get into bed late. To begin, start with 5-10 minutes of strength workout just before you take you bath in the morning or before bed time, you can find a lot of web training pages and I bet that an equal volume of apps for you favourite smart phone. After a few weeks, in your routine, it's up to you, maintain it, increase the workout time, or the intensity of it.
I started with low time consuming training programs like this since you don't need anything more than your own weigh and can be done in our bedroom.
If you have a tight schedule avoid gyms and big groups sports.
Choose a small and loose but steady training program. You can do it.
Most of all be persistent, at first it's hard, if it was easy everybody would do it. But after a time it will be like any other routine.