Yes, the TS4231 is backwards compatible the TS3633. The TS3633 has a single digital ENVELOPE output that indicates anytime the photodiode connected to the TS3633 is exposed to modulated infrared light. The TS4231 has the ENVELOPE output and adds a digital DATA output that follows the modulated carrier being seen by the photodiode. SteamVR Tracking 1.0 systems use only the ENVELOPE signal while SteamVR Tracking 2.0 systems will use both the ENVELOPE and DATA signals. 

Valve will release the Tracking 2.0 system that uses what Valve calls "Sync-on-Beam." All Sync-on-Beam systems will require the TS4231. The TS4231 has a two-wire digital configuration bus that shares the ENVELOPE & DATA pins. After power-up, the TS4231 needs to be configured for appropriate operation. The SteamVR HDK provides software to configure the TS4231 from the Lattice FPGA in the HDK. 

For applications not using the SteamVR HDK, Triad provides an Arduino Library that can be obtain through the Arduino IDE Library manager or downloaded directly from Github here:

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