Can an NDA have a clause in it to prevent hiring employees from your company? Well yes, it is technically possible.
An NDA is an agreement between two companies regarding non-disclosure of intellectual property. What an individual company deems as risk to disclosure is entirely dependent on that company's policies and risk aversion. As long as both companies are satisfied with all of the terms laid out in the agreement, then it can really say anything.
An NDA is about protecting IP from an organisation such that it isn't used by an external party for financial gain. If this organisation sufficiently trusts your company to show you their IP, then there is already a reasonable indication of acceptable risk. If your company happens to purchase Company X's product or service, then that is not so much of an issue as you aren't taking market share away from them.
Now, a non-competition contract is what you are thinking of. This is something that either an employee or a contract partner may be required to sign. Non competition clauses are more commonly referring to not working for competitor organisations for a predefined period of time. Is this a part of the NDA? No, not normally. Is it potentially something that will be signed if your company agrees to purchase Company X's product? Who can say? It is possible that there would be such a clause.
Having said all that!
If you have a potential offer on the table with Company X, then there is a likelihood that they have already considered this outcome and it's either not an issue or one that they are prepared to negotiate around. Given that Company X is the vendor (who owns the IP), then it would be far less likely to restrict hiring employees from a client organisation than if an employee from Company X were to move to a client organisation.
I would suggest not being overly concerned about it unless something more concrete is established, but do NOT give your notice at your current workplace until all or any of those issues have been worked through and resolved.