Yes, a person can be anointed without experiencing the baptism of the Holy Spirit. People were anointed for healing (Mark 6:13; James 5:14), and Christians are anointed by the Holy Spirit to have discernment and understanding of God's word (1 John 2:27).
God can "anoint" people for certain ministries by gifting them in the areas to which they are called. All of these can be done without the heightened experience of the Holy Spirit.
The word "anoint" means several things. In the Old Testament, objects were anointed; that is, they were covered or touched with oil or another means of anointing (Exodus 40:9-11; 30:26; Daniel 9:24;) to signify a special purpose or use. People were anointed with oil in the Old Testament as priests (Exodus 28:41; Lev. 4:5; 16:32), kings (Judges 9:15; 1 Sam. 15:1), and as prophets (1 Kings 19:16).