Permanent installation of Big IP edge client automatically via connectivity profile.

is there any possibilities of permanently installing the Big IP edge client via connectivity profile.

No. It is not possible to do a fresh installation of edgeclient using connectivity profile. Instead you can provide a link to the BIGIP Edgeclient setup file to the end user (either hosted on BIGIP itself or on other servers) so that he can download and install it manually. Alternatively, if the end user is using corporate domain joined PCs/laptops, you can force the installation of edgeclient on the domain users PC/laptop using appropriate GPO on Active Directory.