If you use any of the AT&T apps, they may not work. Also SoftCard requires an AT&T branded phone and a secure SIM from AT&T. If you use Internet Sharing and your plan supports it, you may need to call AT&T to register the IMEI with them or it may not work.
In most areas, you should be okay without LTE aside from the slower speeds. The networks mostly run on separate frequencies. However, in some areas, I believe they use the 1900 band for both LTE and HSPA and you may get a degraded signal with a phone without LTE though most likely it will still work okay.