Can't believe I missed this one when it was first posted.
No, as far as I've been able to tell you can't make a cost-free Policy, other than Finishers (which appear to have an explicit cost override inside the engine, AFAIK). For my own mods I've needed something like you've described, a Policy that acts as a pseudo-Trait, and adding this has not been easy. Here are the things you need to keep track of:
1> If you give everyone an extra policy, then you'll need to change the Culture cost equation. The core game, if I remember right, is 25/5/1.80. If you're adding an extra policy, then you can still get a very similar cost progression by changing these to 16/4/2.01. (Seriously, try it in a spreadsheet, it comes remarkably close all the way up to N=30.) Obviously, since you're asking about costs you're aware of this issue.
2> Because they count towards cost, you can't change the number of extra policies active at a time. So if you want to give one civ a specific Policy, you need to give everyone else a different Policy (possibly one with no effects) to keep it all balanced, cost-wise. And if the Policy is something that's supposed to go away at a certain point in the game, then you'll need to add a second Policy whenever the first is removed. So in my mod, when POLICY_MYTHOLOGY is removed, POLICY_BASE is added in its place.
3a> If you put this new policy as part of an existing Policy Branch (Tradition, Liberty, etc.) then you effectively prevent anyone who doesn't have that custom Policy from completing those branches, which means no Finisher bonuses and no counting that branch towards a Cultural Victory.
Also, the AI has a built-in predisposition to finish any branches it's already started. (In fact, it's basically banned from opening up a third unfinished branch at all.) If you give it a policy in the Tradition branch, for instance, then it'll always try to take the rest of the Tradition policies as soon as possible. This'd severely impact the AI's ability to function.
3b> If you DON'T put this new policy in an existing Branch, and instead create a new Branch to contain it, then a few things will happen:
- SocialPolicyPopup.lua, the UI file that draws the Policies window, will crash as it reaches a branch it doesn't recognize. You have to either disable the plotting of the Branch box in four places within that Lua file, or alter the SocialPolicyPopup.xml file to have space for an 11th box. (Note that the Policies window, and the DDS images it uses, are explicitly sized to combine into a 1024x768 box. If you want to add more area, you'll cause problems for people playing on the lower resolutions, say on a laptop. In my own mod I added a new button to show/hide the 11th box as necessary to get around this.)
- If you only have one policy in that new Branch, it'll always count as a completed branch towards a Cultural Victory for the civs that have it.
- If you have multiple, mutually exclusive policies in the new Branch, it'll no longer count as a completed branch towards a Cultural win, but it WILL count as an "open" branch for the AI, preventing computer players from opening up new branches normally. To get around this, my own mod had to add a Lua override; if the AI is stuck because it keeps trying to buy a policy it can never take (as evidenced by having significantly more culture stored up than is needed to add a new Policy), the mod forces it to buy a randomly-selected available policy, which might mean opening up a new branch. You'd need something similar in your own mod.
Bottom line, yes, it is possible to create a series of Policies to provide a much wider variety of additional Trait-like effects. It's just not nearly as trivial as setting a cost to zero or anything.