Can Log shipping be restored to an earlier full backup point in time?

Hi Guys,

I have 2 MSSQL 2008 R2 STD servers over 2 Geo locations.

I have small amount of changes each day in the DB.

Can I make a full backup once on server1 and copy it to server2. Then copy only the transaction logs without the next full backups?

Will the transaction logs that are written after the next daily full backup will be able to be restored on server2?

Like this example:

Server1 - Full-Backup---TRN1---TRN2---TRN3---TRN4---TRN5---TRN6---TRN7---TRN8---TRN9...TRN10...
Server2 - Full-Backup---TRN1---TRN2---TRN3---Full-Backup---TRN4---TRN5---TRN6---TRN7---TRN8---TRN9---Full-Backup---TRN10...

Thanks,

Michael