Yes, there are companies that will accept if you have a diploma in Computing. But you have to ask yourself, is it really the degree that matters or the knowledge that matters?
Without knowing your candidate in depth, how do you expect your employer to gauge you without a relevant degree? True enough, having a relevant degree does not absolutely determine that a candidate must be competent, which is candidates are often given technical tests to ascertain competency.
In your statement that jobs required degree level understanding + years of experiences, I will answer in 2 parts.
First there are always jobs that assume you are a fresh grad and hence a years of experiences is not always a necessity. However there is often an expectation that s/w engineers have a good understanding of the industry and are equipped with a broad understanding of what are the tools and softwares that are in the industry. All these knowledges are easily achievable just by frequent reading off online articles, news, and forums. With 3-4 years of education on this field, it will be hard to not be equipped with such knowledge. Not knowing in depth can be understood, but not knowing they exist is a different story.
Coming to competency, you have to ask yourself, if 10 candidates are available and the same remuneration is to be offered to all these 10 candidates, why should the employer take someone whom knows less (using the excuse that he/she does not have a knowledge that can be imparted in a degree CS or relevant course)? It is not the degree course that matters here, it is the expectation of knowledge that matters here.
Don’t expect a company to train you as if you don’t know anything. Companies train where it is industrial knowledge that is hard to acquired from institutional learning such as high availability setup, clustered environment, backup strategies, off-site, security strategies and tools, version control strategies, etc. You can’t expect the company to train you on multi-threading and multi-processing concepts, database calculus knowledge, concepts on programming methodologies and so forth.