According to your link:
"This program is approved by the Landscape Architects Technical Committee under the State of California Architects Board to meet the education requirements for licensure in California."
However...
http://www.latc.ca.gov/candidates/genexaminfo.shtml
"Please visit the CLARB website to confirm specific LARE fees, schedules, examination dates and test center deadlines."
Council of Landscape Architecture Registration Boards (CLARB) is really the ultimate say in the proper accreditation of landscape architecture programs, degreed or not, so I would first contact CLARB to make sure this program can count towards LARE qualifications. I also don't see the program listed through
http://www.asla.org/schools.aspx, There are a couple of other things to be aware of. First, are you planning on practicing landscape architecture in another state besides California? Circumstances may change 15-20 years from now and you end up moving out of state. Would other states, which may or may not have different title and practice acts/reciprocity laws and requirements, prohibit you from calling yourself a landscape architect in that state because it is certification not a formal degree? Second, if your end goal is to earn an offer as a landscape designer with the intention of becoming a landscape architect, then you have to convince the employer that your training is credible. I think it is very hard sell to put a certificate program in the same category as a formal BLA or MLA, and potential employers may mistake you as ineligible to sit for the LARE.
Bottom line, contact CLARB and start doing informational interviews with practicing professionals to determine how this program will be accepted. For those of you who practice as landscape architects in CA, are there are other requirements?