No...and if you even TRIED to build a gun capable of launching a bullet into interplanetary space from the ISS, you'd probably destroy the ISS (or severely damage it).
As others have pointed out, an increase of only 400 m/s (the approximate muzzle velocity of a 9x19mm Parabellum fired from a SIG Sauer p226) would be far short of the delta-v needed to escape from Earth's sphere of influence.
The orbital velocity of the ISS is about 7.66 km/s, or 7,660 m/s, and it orbits about 422.5 km (average) above Earth's surface. The escape velocity from Earth, starting at that altitude, is about 11,180 m/s, so you'd need to give the bullet a velocity change of 3,520 m/s in the prograde direction in order to have it escape from Earth's sphere of influence (SOI). That's nearly 9 times faster than the ordinary muzzle velocity. Sorry, but a regular gun isn't going to do it.
But let's say you built a special gun for a special bullet - a one-of-a-kind contraption that could actually accelerate a bullet up to 3,600 m/s (we'll give the bullet a little extra kick just to be sure). The mass of a 9x19mm Parabellum is 7.45 grams, or 0.00745 kg, so it would take an impulse of 26.8 Ns to kick the bullet up to speed. That momentum would be subtracted from the ISS's orbital momentum, but the ISS is so massive that it wouldn't make a huge difference. (The ISS would slow down by about 0.06 millimeters per second, barely affecting its orbit at all.)
But what about the force needed? The typical barrel length of the SIG Sauer p226 is 112 mm, or 0.112 m. The bullet must accelerate from 0 to 3600 m/s over that short distance, requiring an average acceleration of about 5.8x10^7 m/s²...nearly six million gees. By comparison, the NORMAL average acceleration of the bullet is about 73,000 gees. An acceleration of six million gees would require an average force of 431,000 newtons (nearly 97,000 pounds) exerted against the back of the bullet. Assuming the cross-sectional area of the bullet is 0.000064 square meters, that's a pressure of 6.76 Gigapascals, 33 times greater than the pressure normally generated in a handgun.
Now I'm no expert on materials, but I suspect that the consequences of generating so much pressure in a closed container would be catastrophic to the structure of the gun. I suppose the gun would explode violently...NOT something you want to happen on the ISS. Flying pieces of shrapnel would puncture astronauts, sensitive equipment, and the walls. Death and destruction would ensue.
Skipping all that...the best you can do, as you correctly surmised, would be to raise the bullet's apoapsis a little bit.
I hope that helps. Good luck!