Short answer: It is not offensive. You will be pretty well by using your resource.
At least, I don't get offended (I'm American) when reading a web site that was written for Spain; the problem is more subtle.
Spanish is a pretty well standardized language. People from one region can understand (easily) people from any other region. However, we are regionalist. For example, for Mexicans, it is completely natural to hear a Spanish talking like a Spaniard; but we consider very unnatural listening to a Mexican trying to speak like a Spaniard.
In writing the problem is even less important. if you avoid slang, there are only minor differences. But it depends on what are your target readers; if they are Spanish, it's best if you use the es-ES resource file.
Referring to Latin-America you have the same problem; there are many different regional variations so there can't be a es-419. In fact, it is the first time I hear about such a thing (but I'm not a web site specialist.) There can be resources like es-MX or es-AR; there is even es-US.
What I know is that it is possible to put all the resources into a web site and then the server will detect the region of the reader and provide the right translation. Most of the times it is not practical to provide all the variations of the language to your web site so you have to provide those that you have. What is presented when you don't have the correct region or language depends on the configuration of the server (how it is done is not the scope of this site and, of course, it's not what you are asking.)
Many times, the differences are minor. Other times there are differences; for example the word hyperlink in México is hiperliga; in Spain is hipervínculo. So if your budget can handle it, I would recommend, at least:
- one North-American version (e.g. es-MX, es-US)
- one South-American version (for example es-AR, es-CO, es-CL.)
The more you have, the better.
I would also recommend you to ask this in another site like Stack Overflow or Webmasters so you can get the attention of web site developers and administrators.