There are a lot of different kinds of oil burners with a huge variety of tips. So this answer is general, and might or might not apply to your specific burner tips.
The atomization of the oil for proper burning usually, (I say usually) is dependent upon tip sizing and configuration, depending upon what type of atomization you are using.
Steam, air, and mechanical are the most common.
If it is mechanical, I would state that the tip condition is the most critical.
So, if the blasting has any potential at all to alter the tip size, or configuration, you are wise to be concerned.
Tips are generally designed out of very hard materials to resist abrasive wear from the oil, so a light blasting would not, in most cases, do any damage.
However, unless you have a procedure where a blaster operator can't just play that blast stream on the part until it disappears, to use some overstatement, he/she could in some cases cause damage.
There also could be issues with destroying tight clearances that are built into these types of tips.
If you continue to use this process, you should begin an inspection procedure to make sure that the tips are not damaged in the process, otherwise you could have some real burner problems.
Personally speaking, I could blast those tips and not do any damage to them. (I got some experience working my way through school.) But I am not sure I could hand the wand to some one else (Bubba) with the same confidence. Be careful.
rmw