Does WhatsApp disclose the sender's IP address? Is it possible to get it by running
netstat -a or via Wireshark?
WhatsApp uses a client/server architecture based on Jabber (XMPP).
For the recipient(s) to see your IP addresses, the application will have to include your IP address in the metadata of the message. But this has no functional role in the design of such an application.
Your packet capture will likely show IP addresses belonging to WhatsApp(or Facebook) and maybe a CDN company like Akamai that stores media.
Short answer : No. Apart from possibly VoIP calls (from some limited testing the client appeared to perform some reachability tests and connects directly if it can). Mobile networks often use NAT so you often don't have a unique public IP anyway (WiFi would be the only concern).
Long answer : The messaging protocol is documented here and does not contain any IP addresses, it contains the telephone number of the sender to identify the user. Even file transfers are downloading from a HTTPS/TLS server owned by What'sApp. VoIP calls however appear to be able to go directly P2P if the network is open enough which would then reveal your IP. Additionally when on a mobile network you will most likely be going through a NAT so you don't have a public IP address that uniquely identifies you for your IP address to be of concern.