Well going to JJ Hays' book, he gives a small diagram outlining the signal net within the Armd Rifle Coy for September 1943.
The SCR-528 is shown mounted on the Coy HQ halftack (I think this was a vehicle only set), netted to the Bn or relevant Combat Command frequency. Each Rifle Pl HQ halftrack, the Jeep with the Atk Pl, and the Jeep at Coy HQ each then have an SCR-510 (Hays says that was pack or vehicle mounted, Forty's US Army Handbook suggests vehicle only, with the SCR-509 for pack use).
August 1944 the Coy gets extra kit, with an additional SCR-510 for the Maintenance Sect. More importantly there's a 'pool' of six SCR-536 sets, generally allocated as one per Coy and Pl HQ, leaving one spare. The SCR-536 is, I understand, the handie-talkie you mentioned, around 6-lbs in weight with a range of about 1 mile.
To my untechnical eye, that suggests the vehicle net remained largely as was, but they found a need for dismounted comms as well. The issue of six SCR-536 sets was comparable to the allocation for a standard Rifle Coy, and was pretty much 'one per officer' ratio. Hays notes that November 1944, Coy HQ was authorised an SCR-300 (the actual walkie-talkie?), with a 3-mile range. Yves Bellanger's book on US Infantry Div organisation notes that Rifle Coys would normally have an SCR-300 attached from Bn level, so again that seems to extend the practice to armoured troops.
Basically, they could duplicate a Coy level net with portable radios from late summer of 1944 (possibly earlier), though with shorter range than the vehicle mounted sets provided. But, not one radio per halftrack, or one radio per Squad, from what I can gather; comms centered on Pl and Coy HQ, allowing subunit leaders to talk to each other.
Gary