Is is possible to build a recommender system with this dataset?
It is definitely possible to build a recommender system with the dataset you have.

Although there are a few questions.
1. What is your objective from the recommender system?
2. What approach do you want to take with each recommendation?
3. What is the final goal of the recommendation?

Novice Approach:
A very simple approach could be to recommend similar products, for e.g. if a person is looking at a phone A (on website) you suggest an alternative as phone B purely based on the similarity of the product and nothing else.

There are three steps to Recommender System:
1. Query Identification - What to Recommend?
2. Candidate Generation - How many to Recommend?
3. Ranking - In what order to Recommend?

If you answer these questions you will have a fairly good recommender system.