Last I checked, not with StreetComplete. But the OSM wiki has a table of Android apps https://wiki.openstreetmap.org/wiki/Android which column "Record tracks" can be sorted by, to see which apps have that feature.
How I've done similar before is to record a GPS trace with an OsmAnd plugin, upload it to OSM servers, import it as an overlay in the web-based editor on desktop, and used that and satellite imagery as reference to draw in the missing trail.
In a pinch you can also record a trace and edit directly on it in the field with the Android app Vespucci, but its UX is clunky and much less friendly to new contributors than the web-based iD editor.
How I've done similar before is to record a GPS trace with an OsmAnd plugin, upload it to OSM servers, import it as an overlay in the web-based editor on desktop, and used that and satellite imagery as reference to draw in the missing trail.
In a pinch you can also record a trace and edit directly on it in the field with the Android app Vespucci, but its UX is clunky and much less friendly to new contributors than the web-based iD editor.