There are only a few occurrences that Romans ever deployed in a single line, usually it was to extend their line outward to prevent envelopment by mobile enemy, predominately cavalry. Ross Cowan's Roman Battle Tactics lists five examples: Ruspina, Forum Gallorum, it was recommended by Cassius at Carrhae but not done (and quite possibly would have saved the army), and it was used at Nisibis.Regarding the issue of a single line of cohorts... Well, yes, it would have happened on occaision depending on circumstance. Such a line has a fundamental weakness - if the troops waver and flee at any point, the line is disrupted and open to exploitation.
However the Romans were not keen on leaving a battle line so unsupported. At the very least they would try to provide a second line, or better three, or if you're spoilt for numbers, four (though I can't think of any battle off hand other than Cannae when that happened). The deployment was typically in a chequerboard manner, the Roman quincunx.
The Romans typically aligned their own infantry into two or three lines, especially against enemy armies made up largely of line infantry. With that system their secondary line would plan to relief the first line, while the third line would be held in reserve and not used unless the army failed, was routed, and needed to fall behind the third line for protection protection, or if the the first and second line of infantry routed their enemy counterparts and the third line could come and support them.