Do two lesser degrees ever equal a higher degree?

From an educational perspective, community colleges usually do not offer courses beyond a sophomore level. Therefore, the bachelor's degree will probably contain more depth than an associate's degree. For example, an AA in economics will probably stop with intermediate microeconomics, but a BA may include advanced courses in microeconomic theory.

From my experience, in the UK at least. It's irrelevant how many qualifications that you have at any particular level, they never add up to the level above.

For instance, you could have 20 GCSEs, but someone with 1 A Level would still be considered qualified to a higher level than you.

The same goes for degrees, you can't add up Bachelors degrees to make a Masters or Masters degrees to make a PhD.

However, that being said, in Europe we have a system known as the European Credit Transfer Scheme, where you study modules worth a certain number of points (these also have associated levels) and should you change institutions, you can carry over any of these that haven't been assigned to a particular qualification.

Thus, if you studied for two associate degrees and two different institutions but never got awarded them, you might have enough credits to be awarded a bachelors. However, it is doubtful that you would have sufficient credits at the right levels.

Employment: I recommend that you make some appointments with people in your computer programming department for career counseling. If your community college has a person who coordinates Co-op Education, that person would probably be a good starting point.

Of course you can apply for jobs with an Associate's. You won't know for certain how you will fare until you do. (Do take a close look at the requirements for the jobs you are interested in.) But two Associates are not equivalent to one Bachelors. You are missing all or almost all the upper level classes. In addition, some community colleges' courses are not well aligned with those of the state university in the same state. You can find out more about the alignment in your state by asking for a pre-transfer transcript evaluation (note you may do this whether or not you will actually transfer to that school), or by speaking with the person in the state university's computer science department who evaluates transcripts.

Academically: you can't apply for a graduate program without a Bachelor's degree.

Note: Liberal Arts study makes you a good reader, thinker and writer. Your programming classes make you a programmer. The programming classes prepare you for programming (and related) jobs. The liberal arts classes are great for personal growth, but they don't directly strengthen your technical skills.

Take a look at the program of studies in Computer Science in your state university, and you'll see that there's plenty of worthwhile work ahead of you in the second half of your undergraduate studies.