Is Gregorian chant based on speech (when it comes to rhythm)? Despite having sung a few pieces back in my musical days, this question never came into my head and I don't know nearly enough about Latin to make the comparison. It's late here in the UK so am about to sleep, but will Google around a bit tomorrow..
Yes. It is also the case in plainchant in the C of E tradition (the "ancient office hymns" as well as the psalm, the Benedicite, the Sanctus and Benedictus, Te Deum etc.). It is only somewhat stylized so that it can be sung by groups of people (otherwise people's own idiosyncratic rhythms would produce a cacophony), and terminal syllables of verses tend to be held and elaborated, but it is very much based on the rhythms of ordinary speech.
It is at least heavily weighted towards speech like the previous comment mentioned. This is difficult for modern folk to understand. In Anglican chant, the term "Anglican Thump" is used to describe a common problem where singers race in the initial section of the chant up to the cadence and then stop to pound out the last few notes in metered time.