I do not believe it would work that way, since the Steam version and non-Steam PC version are different games, just as you would buy a console version and it wouldn't count as a PC version. The servers are the same, but to be safe, you would want to purchase your ESO membership through Steam. If something were to go wrong, you would then have two companies you could refer to to help you fix any issue you have, too, so if Steam couldn't help, ZOS support probably could (they have some of the best support I've seen). However, if you purchase ESO+ through the website and not Steam, ZOS might be able to help you, and might not. I cannot test this myself, as I don't own a copy of ESO through steam, but without a ZOS mod or someone who has tested this, the only answer is to test it yourself (and if it doesn't work ask ZOS support for a refund), or just buy the sub through Steam and trust in the support staff to get you through any of those issues you've read about (if you encounter them).
Actually I've only ever had issues when I bought subscription or crowns directly from Steam. I always buy everything through the eso website now and it works just fine. Steam and non-Steam versions are exactly the same since your accounts are automatically connected. You can use both methods but Steam support is more annoying to deal with if you run into trouble in the future.