Can National Guard units still get attached to active duty while deployed?

Answered in para 19-17 of AR670-1
"...(3) Unless otherwise approved by this regulation, Soldiers attached or under operational control (OPCON) to other services are not authorized to wear their patches as their SSI–FWTS without written approval from DCS, G–1 or a desig- nated representative.
(4) Soldiers of all Army components (Active, ARNG, and USAR) who deploy during periods of service designated for wear of the SSI–FWTS are authorized to wear a SSI–FWTS. There are no time-in-theater requirements for authoriza- tion to wear the SSI–FWTS. Soldiers may not earn more than one SSI–FWTS during the same deployment.
(a) A deployed unit (company or higher) will wear its unit SSI as the SSI–FWTS, regardless of the headquarters ele- ment deploying and the unit alignment or OPCON during the period of deployment.
(b) A deployed unit will not wear its assigned SSI as its SSI–FWTS when the SSI belongs to a major command, such as an ACOM/ASCC/DRU or State area command, or a non-deployable unit. In such cases, the unit will wear the SSI of the lowest echelon Army unit (company or higher) in the deployed chain of command as the SSI–FWTS. When there is no intermediate unit (company or higher) in the deployed chain of command, these deployed Soldiers will wear the SSI of the senior command in the theater as its SSI–FWTS.
(c) When echelons below company level (such as teams or squads) deploy, members of these units will wear the SSI of the lowest echelon deployed Army unit (company or higher) in the deployed chain of command (based on written or- ders) as the SSI–FWTS. When there is no intermediate unit (company or higher) in the deployed chain of command, these deployed Soldiers will wear the SSI of the senior command in the theater as its SSI–FWTS.
(d) Individual Soldiers who are attached (to include OPCON, cross-leveled, assigned, or augmenting deployed units) will wear the same SSI–FWTS worn by members of the deployed Army unit (company or higher) to which attached by written orders. A Soldier who is further attached (to one or more units) during one deployment will only wear the SSI- FWTS for the first Army unit (company or higher) to which attached by written orders. Soldiers who deploy with their unit (company level or higher) will wear the SSI–FWTS as outlined in paragraph 19–17a(4)(a), regardless how many times they are further attached to other units as individuals or teams. Members of trial defense will wear the SSI of their respective commands as their SSI–FWTS...."

Can they be attached to AD units? Yes.
Does this entitle them to that AD patch? No.

I think it was part of an After Action Report after the 1st Gulf War ( I was full-time NG then, but my memory gets interesting) of an easy award for NG and RC, to attach them to AD units and award them the Cbt Patch - my real Cbt Patch was 3rd COSCOM, and I have orders for my 4th ID Cbt Patch. Others in my Co had orders for other units. NG HET driver, Iraq '03

The NG units weren’t attached, the NG deploys as BCT’s of their own. However, some NG units are aligned with AD units and will wear their patches. That’s a more recent development though.

Early on in GWOT rules meant for the way we used to deploy (full units) were in effect and you could wear you HQ SSI. Those rules were based on large unit deployments where attached unit become part of a larger one. In the past 20 years we have become modular so the old rules no longer applied and 670-1 was changed to essentially say that Company level units will deploy wearing the SSI they already wear. We are modular now and can have the 101st as Div HQ with brigades under their command from 1st ID, 2CR, 82nd or any brigades under their command including Guard combat brigades. In the mix can be companies from the Reserve and Guard that wear their own patch. The problem is also with Marine patches. Only a couple Marine patches are authorized for specific units at specific time frames yet I've seen Soldiers (AD, USAR andARNG) just throw on a Marine patch.

If he was attached as an individual or unit smaller than a platoon he could be authorized. Most likely he just got a memo thrown in his record so he could wear a named brand patch on his right arm against Army policy. This is fairly common in the RC.