Are there transitive/及物动词 or intransitive/不及物动词 verbs in Chinese?
I don't think "What do you think" is really a suitable question here... So I'll address the question in the title instead ("Are there transitive/及物动词 or intransitive/不及物动词 verbs in Chinese?"):

Sure there are. And I really doubt they are "mostly" separable verbs.

For instance: 他走了 "he left", or 花開了 "the flower blossomed". There are a large number of such verbs that seems quite clearly intransitive. There are also many that goes both ways like in English. The character 吃 for example is by itself also a verb (in contrast to your example of 吃飯), and it can be both intransitive: 我吃了 "I ate", as well as transitive: 我吃派了 "I ate pie".

You claim regarding 參加 or 游泳 taking adverbials of place instead of objects seems highly suspect to me. I fail to see what is adverbial about 比賽 in 我參加了比賽 "I joined a tournament".