I suspect that by "plantlets" you are meaning reproduction by the inflorescence, as opposed to reproduction by runners. Both forms result in what I usually call daughter plants, or plantlets, somewhat interchangeably.
All Echinodorus use one of these methods, as well as the more "normal" sexual flower/seed. The will not (as far as I know) produce flowers when grown submersed, only when emersed. In their natural habitat they are all bog plants, amphibious, spending about half the year emersed during the dry season (when they flower) and half submersed during the flooded months.
When grown submersed in the aquarium, those species that produce an inflorescence emersed still do, sometimes once a year and sometimes more often. But instead of flowers at the nodes, plantlets/daughter plants appear.
Dr. Karl Rataj, who arguably knows more about this genus than any other botanist, revised the genus in 2004. In his published book on the revision, Dr. Rataj follows Fassett (1955) in dividing the genus into two subgenera, namely Helianthium and Echinodorus. The first contains two sections, Tenellii and Nymphaeifolii. The latter of these holds one species, E. nymphaeifolius, while the former holds nine (similar) species including E. tenellus which is the type species for the group. He states that the species in this section, unlike the other species, propagate mainly vegetatively by long rhizomatous runners up to 50 cm long, with new plantlets at intervals of 2-5 cm, regardless of whether they are cultivated emersed or submersed. Plantlets sprouting from the inflorescence are relatively rare. In nature these plants grow mostly in swamps, with emersed forms flowering regularly and forming achenes. Constantly submersed plants are sterile and reproduce only vegetatively. [cited from p. 5]
In the 15 or so years I have been cultivating E. tenellus and E. quadricostatus they certainly have never produced an inflorescence but the runners are very frequent. All of my plants of the latter species in the 115g and of the former species in the 90g are descendants from single plants I acquired in the mid-1990's.
Hope that answers the question.
Edit: Just noticed I didn't respond on the matter of E. augustifolia--which is actually E. angustifolius as described by Rataj (1975). It is within the Tenellii group, so yes, same as E. tenellus and the related species.