There are many firms and smaller offices that have positions for paralegals or legal secretaries, including those that will train you coming out of college if you commit to two years as you mention.
I did not do one of these programs, but I have worked as a paralegal. I absolutely recommend doing this prior to attending law school. First, it helps you know whether this is what you truly want to do and may give you insight into what type of law you are most interested in/good at so that you can pick courses later on in those areas. Second, work experience only boosts your application and matures you, which many coming from undergrad need. Third, this will boost your job application later, including helping you make connections in the legal field in the market you presumably wish to work after law school.
I could go on, but those are the major points. Even if you don't get it with a major firm, look at smaller and mid-sized ones. Honestly, I would recommend a small firm over a large one for this, since you are more likely to develop close relationships and do true legal work beyond secretarial duties. (I worked in a small law office and was able to prep for court, attend court, do individual client meetings, and much more. People who are one of the crowd at a large firm don't typically get that chance.)
Interested in how much of a boost firm experience gives one come OCI and beyond. Besides the connections (I imagine less important if you do not attend school in the same market that you worked at prior to matriculating), can anyone comment whether the fact of having previously been employed in a legal office helps demonstrably, or only negligibly in getting a future position at another firm? Is it worth pursuing solely on that consideration alone?