Great nostalgic question; it’s been a long time since I’ve interacted with a DD 1149.

Typically most transactions regarding property and contractors now is recorded using one of the property related applications in the PIEE (Procurement Integrated Enterprise Environment).

Bottom-line up front:  They can, but it's not advised since individual contractor personnel cannot be held liable.  Only the contractor organization can; property is accountable to contracts not individuals.  In my experience, they would often be sub hand receipt holders rather than HRH.

References:

DA 3161 see DA PAM 710-2-1 (see chapter 5)

DD 1149 see DoDI 4161.02

FAR Part 45 and DFARS Part 245

DoD Instruction 5000.64 is silent on the subject of contractor employees being primary property custodians (hand receipt holders). According to the Property & Equipment Policy Office (AT&L), DoD policy does not prohibit contractor employees from being primary hand receipt holders. We suggest DoD Components evaluate the risk to the Government relative to loss of Government property prior to appointing a contractor employee as a primary hand receipt holders. Unlike a Government employee (civilian or military), when a contractor employee signs a hand receipt it does not mean that he/she can be held financially liable for the property if it is lost, damaged, or destroyed. Contractor organizations, not their employees, have stewardship responsibility for Government property provided under the terms and conditions of a contract. The contract includes loss provisions through the incorporation of clauses such as the Government property clause of FAR 52.245-1. Under certain circumstances, the contractor organization can be held liable by the contracting officer for “loss of Government property” as defined in FAR 45.101 and FAR 52.245-1(a), but never a contractor employee. If property is in the possession of, being used by, and controlled by Government employees it is not Government-furnished property (GFP). By definition GFP is furnished to the contractor for performance of a contract. GFP must be identified in solicitations and awards (contracts) in accordance with FAR 45.201 and DFARS Procedures, Guidance and Information (PGI) 245.103-72. If property is not accountable to a contract there is no contractual coverage and the loss provisions of Government property clause (with or without its Alt I) do not apply. Government property can be considered incidental to the place of performance when contractor personnel are contractually required to be located on a Government site or installation, the property is used within the location, and the property remains accountable to the Government (using Government internal controls). Neither FAR Part 45 nor the Government Property clause apply to property that is incidental to the place of performance.