Free 2 Day Xbox Live Gold Trial for the Xbox 360.

Yes, you certainly can. The bottom of a 2 Day Gold Pass states the following:

XBOX LIVE 2-Day gold Membership, free trial allows access to these Gold features: online multiplayer gaming, Netflix, ESPN on XBOX Live, Facebook, free game demos, exclusive discounts, promotions and video content.

Free 2-day trial offer is only for use on the XBOX 360 and is not valid for current XBOX Live Gold Members. At the end of your 2-day trial period, your membership will default to the FREE XBOX Live Membership, unless you elect to extend your XBOX Live Gold
Membership.

Now what this doesn't tell you is that you cannot play in ranked matches with the trial membership, but you are free to play in social matchmaking playlists for games.

Hi there,

The Xbox Live Trial codes are available when you purchase games or console bundles. The prepaid code for the free trial can be a 2, 3 or 14 day Xbox Live Gold trial membership. To know more about Xbox Live Free Trial
membership, you may go to How to get an Xbox Live Gold trial subscription.

I hope this helps.

Hi there,

only a standard Xbox Live Gold subscription will allow you to get a Game with Gold for free. a 14 day trial is like the name mentions a Trial subscription and won't allow you to get a 360 Games with Gold game for free, you will require a standard Xbox Live
Gold subscription for that.

It would help if you read it correctly

14day trials aren't gold trials

Games with Gold available if I'm on a 30-day Xbox Live Gold credit card trial?

You're eligible. You must have a current Xbox Live Gold membership or an Xbox Live Gold trial that requires a credit card.

What kind of Xbox Live Gold trials are eligible?

You're eligible if you're on an Xbox Live Gold one-month free trial.

If you're on a 14-day prepaid code trial, you're not eligible. You must have a current Xbox Live Gold subscription or trial that requires a credit card.

What if I'm on a 14-day prepaid code trial and I upgrade to Xbox Live Gold during the trial period to take advantage of a free game offer? Will I get the game?

If you upgrade to Xbox Live Gold during your non-renewing trial period, your Xbox Live Gold membership won't start until the end of your free trial. You won't be eligible to download a currently offered free game until your trial period ends and your paid
membership begins

if u buy a xbox console then u will get given a 14 day free trial but xbox dont give away 14 days free trial for xbox live gold