Yes, you can still restore up to Log_6 using the same sequence you described earlier, or you could restore using that 'other' backup and subsequently just Log_5 and Log_6.
A full backup affects only the base from which your differential backups need to restore from. E.g. if a full backup was taken between Log_2 and Log_3, then Diff_1 would require that you restore that full backup first. Full_1 would be rendered redundant for Diff_1, unless that other full backup was made using the COPY_ONLY option.
A full backup affects only the base from which your differential backups need to restore from. E.g. if a full backup was taken between Log_2 and Log_3, then Diff_1 would require that you restore that full backup first. Full_1 would be rendered redundant for Diff_1, unless that other full backup was made using the COPY_ONLY option.