Is the process of adding new parallel (matching) cells into an already built battery pack safe?
Yes, it can be safe but it must be done correctly.
Assuming the pack really was just built and hasn't been put into service yet, then you can add additional cells in each parallel group while they are still connected in series.  In the absence of any load across the series terminals of the battery, there is no difference between adding the cells to each parallel group in isolation (the series connections to any other parallel groups cut), or doing so with them connected in series.  The batteries don't 'know' that the series connected cells even exist at all unless or until series current is actually flowing through the entire battery.
That said, after you have added the additional parallel cells, you must perform a balance charge on the entire pack.  There will always be some error in how closely matched you're able to get the voltage of the new cells to the existing parallel cell groups.  If these is towards the upper end of the state-of-charge curve (near 4.2V), a small voltage difference can represent dozens of mAh of difference in a cell's state-of-charge.
In other words, once you've added the additional cells, each parallel group is probably not going to be at the same state of charge anymore.  They won't be wildly different or anything, and might even seem very close, but even small difference can grow increasingly large with time as the pack ages and is cycled.  So you'll want to rebalance each series-connected parallel group to ensure each group is charged to the same level again.
And of course, you will need to ensure the maximum charge/discharge current ratings will be observed and some current will flow  because, as said earlier, it is not particularly realistic to expect to get the terminal voltages perfectly matched.  The current will the limited by the parallel internal resistance of the new cells, as it will only be these added cells that will be at slightly different voltages.  Check the cells' datasheet for the internal resistance and maximum charge/discharge current.  That should give you an idea of how close you need to match the voltage to be safe.  I think it would be unlikely for a difference of 100mV or less to result in too much current, but if you aren't confident that you can match the cells that well, then you should temporarily connect them through low value resistors between one of the terminals and the rest of the parallel group (so connect positive of the new cells to a resistor in series, and the other leg of the resistor connects to the positive of the existing parallel group).  Connect the negative terminals directly.  Or vice versa.  Once they've done most of their equalizing through the resistors, then you can go ahead and welding them into the final assembly.