To be able to arrive at the solution to this colossal question of whether it is OK to use your phone while it is plugged in, you need to understand the science behind it.
Phones these days use either NiCd or NiMH or Li-ion batteries (wraps up 99% of mobile phone batteries on earth). Every battery has terminals, one positive terminal and other negative. Now we know that phone tends to heat up while charging, this is due to imperfect conversion of electricity flowing from charger into Charged electricity stored in the phone battery (Energy losses, et al). As the overall battery temperature goes up, the chance of battery to explode still remains bleak. But in case there is any other reason for battery to blow up, this heated battery will be an added advantage to the blast.
So now we know that technology isn’t faulty, next culprit is errors or imperfection in battery fabrication. This is the single most common defect observed in exploding battery cases. There might be deposition on battery terminal which may lead to short circuit and hence an explosion. Irregularities in battery quality, especially in unbranded batteries is a big problem. This can be prevented by vigilant buyer who do not fall for cheaper batteries with faulty circuits.
Second culprit is your phone charger. Again the quality of your charger plays most important role. Bad quality charger will heat up excessively while converting your AC mains current into DC and blow or melt itself with passage of time. Or it will loose control over frequency of current being fed into the phone battery leading it to behave in unexpected manner.
In a nutshell, try to avoid using your phone while charging not because there is a risk of blowing it up, but for your own safety. Who would like putting a hot phone to their ear? And as you kep using your phone while charging, the charging process will slow down and lead to extended period to reach full charging.