2003 Honda Accord A/C won't blow cold air

Hi Bluefunk, Welcome to 2carpros and TY for the donation

They should have ran a detection leak if its actually leaking somewhere. If you don't hear the clutch engage the compressor when you turn AC on-have the low and high pressure checked this will determine the amount of freon in it if okay check if the clutch is getting power if so and not engaging the compressor its no good

First the leak must be found. AC systems are closed systems meaning there can be no access to the outside atmosphere. There are many reasons that AC systems leak. One, is a hole in the condenser, but the hoses could be worn from age, o-ring seals can be bad, among other things.
To find the leak-- a vacuum must be applied to the system with a vacuum pump for at least a half hour or so. This makes the atmosphere inside of the system almost zero. Without getting too technical, this is done to boil off moisture in the air, because moisture will cause serious damage to the system. In the process of applying a vacuum, a leak can be pretty easily detected. Take your car to a shop that can apply the proper vacuum to the system and they should be able to find the leak. If a shop does not know how to, or does not apply a vacuum to the AC system, then they have no idea about Ac systems - and I would not take my car there.
Also, just adding refrigerant to a system with a leak will turn the refrigerant to an acid -- because the system is open to the outside atmosphere (which has moisture in the air). Moisture inside of an AC system in VERY bad. The receiver/drier should be changed, and the system should be properly flushed out to get rid of any acid that may exist within the system. The compressor oil should be drained and examined to see if there is any debris inside of the compressor. Black oil in the compressor causes "black death" (a term any AC mechanic will be familiar with).