All of the primary sources discussing this concern (cited and discussed here), apply it specifically to a bed, and make no mention of sleep being a factor at all. These include the Bavli (Pesahim 112a), the Yerushalmi Avodah Zarah (2:3), Rambam in Hilkhot Rotseah Ushmirat Nefesh (12:4), the Tur YD 116, and the Shulhan Arukh YD 116:5.
This strongly implies that this concern would not apply to under a seat on which someone falls asleep, since a seat is not a bed. At the minimum it would imply that the case of a person falling asleep on the bench would be no worse than a case where there is no sleeping person, since sleep does not appear to be the operative factor.
The only possible reason to be stringent would be the possibility that the seat is considered a bed.[i]
This is the view adopted by this kof-k article (page 7), see the sources in notes 63-4.
[i] Which seems unlikely; this isn't a halakhic issue where some other topic may be relevant in defining the relevant terms; it is an isolated passage that defines its own terms. Accordingly, presumably a bed is a bed, and a chair is a chair.