You wouldn't be causing any links, but you could potentially be compromising the integrity of your computer. There have been "free" proxies/vpns in the past who steal client info and create botnets to distribute malware. So, you have to be careful what service you choose.
Anyone can setup a proxy server, and the administrator of said proxy server is easily able to see all traffic coming across the network. Nothing is usually encrypted with proxies.
Ommpa if this can be of any help I have managed 10s of GMails accounts bought from US on fiverr (US phone verified) with my Italian IP and got no issues at all.
They were all linked by me since I did not changed user account nor IP... got 0 problems.
I see more issues coming from a cheap proxy than with your own connection.
Keep using proxies and you could potentially run into issues. They'll keep asking you for verification of the account and recently Ive even run into a situation where one of my buyers who used a bad IP solution received an email from google telling him the google account was suspended - oddly enough the gmail account itself was not...
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AGED SUPER HIGH LIMIT ACCOUNTS: 10,000/$1,000,000 and 25,000/$500,000
And if a proxy gets tied to something illegal by another person or so, you could get pulled in by your use - rare occurrence, true but why not avoid if possible.
Probably not a big deal if you don't do it a lot but I personally wouldn't manage my accounts through it due to lack of security.
A VPN however is a better bet.. I use https://www.privateinternetaccess.com/VPN and find that it's great! It's not eBay/PayPal or Amazon friendly but it's good for anything else.
free proxies, how safe for email 
