EDIT: Based on the information you added in the comments you fall under the first scenario. Even leaving it behind in the US with LogMeIn installed (which im not actually sure you can do without admin access) will not ensure your location being hidden. I don't believe it likely they will notice, it would have be one very vigilant system admin to catch you, but again due to you not having root it is technically impossible for you to fully conceal access from another country regardless of what method you use.
Given your situation the 'leaving it behind in the US with a remote tool' option is the most viable/secure/hidden way to go should you decide to chance it. Proxies are not applicable since those generally only hide web-based traffic, based on your description you need a full point to point tunnel of ALL network traffic originating from your machine. All kinds of headaches come from trying to create 2 VPNs layered on top of each other, one to first hide your address and then trying to initiate a 2nd VPN to the corporate network, add the fact that they essentially own the box you're on and it starts really not looking so good.
Not enough information about your setup to make a detailed recommendation but here goes. Answer is dependent on what you meant by not having admin rights:
- Scenario: You dont have admin rights on the machine behind your router, the machine that will originate the VPN connection.
There is no way to ensure your location is hidden.
- Scenario: You do have admin rights on the machine behind your router.
It can be done reliably, however now it depends on what type of VPN connection you use to connect to their network. One option that will work for almost any situation is leaving a PC behind with a friend or relative with LogMeIn or some other remote tool installed, and then just remote into that machine and originate your VPN connection from there. Fairly fool-proof, as long as you can trust the person you're leaving it with.
There are other options such as a dedicated VPN provider based in the US, but can't say it would work without knowing what type of services you're accessing over the company VPN.