No, it’s not ok to not include dates on a resume. Employers need to know when you held each position and how long you held it to determine whether you’re worth bringing in for an interview.
However, removing the exact months of employment from your resume’s work experience section is acceptable. But you still need to include the years you held each position for.
If you want to further downplay the dates on your resume, use a functional resume format. Functional resumes take the reader’s focus away from your chronological work history, and instead highlight your professional skills and expertise.