Is it possible that Clients (Chrome) will accept the HTTPS connection
using a self signed certificate?
Yes. You need to import the certificate into Chrome (after exporting it to a file, if you have not done that yet). You can import certificates in the certificate dialog, which you can reach via Settings / Advanced / Manage Certificates.
- Since Chrome 58, the self-signed certificate must have the right domain name in the Subject Alternative Name (SAN) field.
- After importing the certificate, you need to restart Chrome.
For details, see for example this question on StackOverflow: