Unfortunately, yes, if the USB 2.0 device seeks the USB-IF certification, it must obey the sequence 100mA -> USB_connect -> enumerated/configured -> full draw of port current. The "full draw" however should be determined by sensing the value of pull-up on attached CC pin.
If the attached cable is a "legacy cable" compliant to Type-C specifications, it should have 56k built-in pullup (you generally don't need any adapter, the cable has the pull-up).
If the attached cable is the "Type-C Standard Cable" connected to another Type-C port, the CC pull-up will be defined by the sourcing port, whichever it is capable of, 1.5 or 3A.
If you want your device to be practically charged, and charged faster, it is advisable to implement a battery-charging detector IC, at least to determine if the port supports Chinese-style charger signature, D+ connected to D-.
To really comply with USB-IF test specifications when using Type-C connector, you need to consult very carefully with this document, Type_C_Functional_Test_Specifications. This is an evolving area, so check for updates.
But if you don't bother with exhaustive USB-IF certification (as most manufacturers do), just take 500mA if it is enough for you, since every reputable host USB port must unconditionally support 500mA of sourcing (except nearly non-existing subset of low-powered portable gadgets running form tiny batteries).
There are two NON-CONFLICTING requirements in USB specifications.
First, a USB DEVICE must not draw more than 100/150 mA from USB port before it gets enumerated and finally configured. Then, if its power requirements fit into host budget (and the host knows what it is), the device can use more. Otherwise it won't be configured and used by system.
Second, a USB HOST ports must be able to supply much more current. From Section 7.2.1, "Systems that obtain operating power externally, either AC or DC, must supply at least five unit loads to each port.".
So, if your USB HOST has a AC-DC adapter or is plugged into AC outlet, or has a massive battery, each USB 3.0 port must be capable to feed at least 900 mA.
If it is a skinny smartphone, it depends on how the manufacturer feels about battery life of their product.
Best Answer
From an official point of view, if you use a USB3.X Connector you should be able to get USB3.X Functionallity since in the USB Certification you would need to also test the superspeed portion of your device.
If a device is superspeed the D-/D+ lanes are NOT used for power, they are in idle state once USB3.X Traffic is going on.
So if not looking at the official standard, your implementation should work when using High Speed lanes and the Power of the USB3.X. but I would not recommend this !
Another thing I would like to suggest is using a Type-C(tm) connector and looking into the power rating of this, might be more suitable for your specific requirement instead of creating a Half USB3.X the power would depend on the hosts RP configuration(500mA or 1500mA or 3000mA)