From the perspective of a Second Life user, a typical roaming bot just comes and goes. They're typically on a region for less than a minute, and they don't interact with anyone or anything. Some try to stay "out of the way"—arriving at high altitudes, for instance—but most just land wherever they land. Sometimes one will get "stuck" or malfunction and stay on a region for some time. Most have a lower impact on sim resources and performance than a typical human-driven avatar.
Roaming bots are almost certainly all operated by Second Life users, not Linden Lab. There's a persistent myth some (or all) roaming bots are operated by LL to generate the inworld World Map (there's a historical coincidence that led to that theory). However, it's not true: as of October 2019, Linden Lab publicly confirmed that "at present" the World Map does not use any processes that would be visible to users inworld. Yes, the World Map was retooled in 2021 but not in a way that needs bots.
Under the Linden Lab Bot Policy, bots are allowed to do just about anything but buy mainland, spam users, and artificially inflate traffic statistics. Linden Lab requires bots be registered as "scripted agents," but SL users cannot directly see if that flag has been set for an avatar.
My analysis of roaming bot activity since early 2019 strongly suggests the majority of roaming bots are concerned with land ownership and/or other properties of inworld land, including the individual or groups that own regions and parcels, when those parcels change hands, and (in some cases) properties of the parcel like the ability to rez, object entry, ban lines, etc.
Most parcel information is only available in Second Life by sending an avatar to a region; regular revisits would be necessary because Second Life land can change and turn over very quickly. So, this suggests many roaming bots are operated by virtual land dealers keeping an eye on the market (and competition)—after all, virtual land is one of the few areas of SL where there's real money. More than likely, the operators collate on-site data with sale and rental listings—ironically, bots are also the best way to get that information, though they need not roam to get it.
A few bots are associated with specific Second Life products (like Triple Labs' Explorer HUD) and others may be used by long-standing services like Tyche Shepherd's GridSurvey. A few others patrol public roads and waterways (likely mapping and/or checking for barriers to passage like overhanging builds or banlines); a handful more claim to be part of various mapping projects.
One bot operator has claimed to collect avatar names from estate and parcel whitelists/blacklists, as well as map individuals' group relationships between communities. I haven't yet substantiated that claim, but it's certainly possible. Another has mentioned using a similar technique to identify various automated and semi-automatd avatars that target the various "free Lindens" traffic-generating games.
My own bot (Loubottin) collects (fully anonymous) statistical info about avatars.
TL;DNR: Almost certainly not.
With enough bots, it's technically possible to try to track avatars around grid. However, besides being a violation of Second Life Terms of Service, such an effort would require a very large bot cohort. I would certainly notice them, and so would Linden Lab governance. None of the cohorts I'm tracking come close. In fact, the total number of grid-roaming bots I track doesn't come close. Yes, I know you might see bots all the time—as of early 2021 it's not unusual for regions to see a dozen visits a day, sometimes far more. But I'm pretty sure this song isn't about you. Or me.
Moreover, someone with the technical skills to run a bot cohort could use other, more-effective ways to stalk Second Life users.
What about metadata? Could a group of bots teleporting around the grid build up a database of locations where particular avatars have been seen and generate a graph of potential connections between them? Yes: that's possible within some limits. First, grid-roaming bots can't go everywhere: bots get banned all the time, and there are lot of private/restricted regions where bots simply cannot go. Second, unlike beacons used by Internet companies like Facebook, Amazon, and Google that automatically track people all around the Internet (often without users realising it), bots actually have to get in the same region as avatars to detect them. Second Life isn't really very large, but most people spend only a few hours inworld at a time. The potential data available to a group of bots is always going to be piecemeal and incomplete. But yes: over time, a group of bots could build up location and association profiles of avatars from public information accessible to them.