Technically you can employ the same approach that Low Reorder implements for you, but natively you’d have to jump through some additional hoops:
1) you’d still need to create a field that is explicitly for ordering purposes - a numeric field, for example, which is really all Low Reorder is doing anyway
2) you’d then have to go into each entry and enter the number into that field - there’s be no way natively to see the order of all of your entries since you can’t add custom fields to your edit list view in the CP natively (Zenbu is an add-on that does give you that ability)
3) and so tied in with there, thee would be no drag and drop ordering, for example - you have to do it manually - not as much of a pain as with jigging the dates, but not hugely more convenient either.
So yes, you can do it natively to be certain, it’s just not quite as quick to set up nor is it quite as convenient to manage - it’s a critical functionality I’d love to see added to EE, as choosing the order of your entries is vital for a CMS, whereas ordering exclusively (or by default) by date is a bit of a blog throwback.