If the vias are well plated they will also make contact without solder but I always solder them. The main reason is mechanical stability: when you use the loop to hook in test equipment there will be quite some force and torque on the test point. Thus you want to use solder so your test point does not snap out during testing.
As with other through-hole components, the test points should be soldered to the board. You could just leave them sitting in there, but you risk poor contact (resulting in incorrect readings) and even worse, they may fall out entirely.
Looking at the top left part of your attached diagram, you can see the legs of the test points are pressing against the sides of the hole. The legs can be bent at different angles, and you cannot be sure that they will stay put.
I have used those test points many times before. They are designed to be soldered to the board. The spring contacts are only supposed to hold them in place during soldering. If you leave them unsoldered, they may not make good contact and can pull out easily during testing, especially if you connect alligator leads or a scope probe to it.
I find this rather an odd question.
You had better HOPE they are meant to be soldered in. The alternative would be an extra step in manufacturing to mask them out while the board goes through the soldering machine.
Generally through hole metal parts are intended to be soldered unless specific wave flow soldering instructions are indicated in the specification.
Further, these parts are not hard to insert, and are therefore not hard to come out when a scope probe is dangling from it. Soldering provides the required mechanical stability you require.