If you add cron task to root's tasks (like in example below) or if you run it with you account and write to your homedir then no, you don't. You need to set permissions only if you want to write somewhere you don't have permissions already.
█ Supportex.Netserver management, full range of services. EU-based outsourced company. Since 1998.
█ Outstanding quality for high performance projects; clustering and high-availability solutions, DDoS protection.
█ Cisco/Junipernetwork management & deployment assistance. Network design and monitoring.