Yes they do take action.
The following is from the PayPal Terms:
"16. Limiting accounts
16.1 If you have a personal account and we have reason to believe that it is being used for a purpose other than a personal, domestic or household purpose, we may limit or close your account or require you to upgrade to a premier or business account.
16.2 If we hold a reasonable belief that there is an increased risk associated with your PayPal account or other service you receive from us or a Related Body Corporate, we may limit your access to sending, receiving or withdrawing funds or using guest checkout or direct Credit Card payment processed by PayPal for up to 180 days. We may take these actions beyond 180 days if we reasonably believe the risk still exists or are prohibited by law from releasing funds or unrestricting your account.
16.3 We may limit access to sending, receiving or withdrawing funds from your account if it is associated with another account or service you receive from us or a Related Body Corporate (including another PayPal account or an account you hold with eBay) which has been limited, is not in good standing, or poses a risk to the integrity, security or reliability of us or our systems. We may determine your PayPal account is associated with another account or service by comparing information we or our Related Bodies Corporate hold about you including names, email addresses or IP addresses.
16.4 The following is a non-exhaustive list of events which may lead to your account being limited:
Reports of unauthorised or unusual Credit Card use associated with the account;
Reports of unauthorised or unusual bank account use associated with the account;
Abuse by a buyer of the reversal process provided by the buyer’s bank or Credit Card provider;
Abuse by a buyer or seller of the PayPal Buyer Protection Policy or PayPal Seller Protection Policy;
Multiple disputes received regarding non-despatch of merchandise, non-delivery of services, merchandise not as described or problems with merchandise shipped;
Receipt of potentially fraudulent funds;
Facilitation of fraudulent activity;
Excessive disputes or Reversals;
Attempts to “double dip” by receiving funds in a dispute both from us and through a Reversal or a refund from the seller or a third party;
Refusal to cooperate in an investigation or Confirm Your Identity when requested;
Initiation of transactions considered to be cash advances or assisting in cash advances;
Sending unsolicited emails or posting referral links on websites where they are not permitted;
Material breaches of this Agreement or its incorporated policies;
A risk assessment of your account conducted by us;
The name on the Nominated Bank Account or Nominated Card not matching the name on your account;
Return of an incoming electronic funds transfer for insufficient funds or incorrect bank details;
Use of an anonymising proxy;
Reports from credit agencies of a high level of risk;
Use of your account is deemed by us, Visa, MasterCard, Discover or American Express to constitute abuse of the Credit Card system or a violation of Credit Card rules, including using our system to test Credit Card behaviours;
Logging in from a country not included in PayPal’s permitted countries list;
The occurrence of an Insolvency Event;
Failure to provide us with information about you or your business activities that we may reasonably request; and/or
Any other activities which we reasonably deem as high risk selling or receiving activity.
16.5 In assessing a risk, we will investigate your account and consider the reasonable risk of a Reversal, a breach or likely breach of this Agreement, or other potential losses occurring to us or our users.
16.6 If access to your account is limited, you will be notified and may be requested to provide information relevant to your account, a transaction or your identity.
16.7 Following our investigation, if we reasonably believe there is no longer a risk, we will restore access to your account, subject to any other actions we may take in accordance with this Agreement.
16.8 If we reasonably believe a risk still exists, we may take various actions to protect PayPal, our users, a third party, or you from Reversals, fees, fines, penalties, legal and/or regulatory risks and any other liability. The actions we may take include but are not limited to the following:
a. Return funds to the sender and restore access to your account;
b. Continue to limit your account access to protect us against the risk of Reversals, legal and/or regulatory risk or because we may be prohibited by law from releasing funds or unrestricting your account;
c. Close your account by giving you notice and returning any funds held in your balance to you minus funds in dispute. If you are later determined to be entitled to funds in dispute we will return those funds to you; or
d. Refuse to provide our Services to you in the future.
16.9 Ongoing failure to Confirm Your Identity may mean we are prohibited by law from releasing funds or unrestricting your account. Any funds in your account will be subject to applicable laws regarding unclaimed monies."