No, you will not face any problems just because you purchased the plan online. Every insurance company has a centralized customer service team that attends to all customer queries/complaints. They do not differentiate between customers who have purchased online or offline. The Claims Management division of the insurance company processes the claim without questioning where was the policy purchased from.
It is important to understand that it is only the mode of sale that has changed. There is no change in the conditions of the policy. Just like a few years back, you had to buy an airline ticket through a travel agent; till some time back even insurance plans could only be purchased through some agent or broker. With the internet becoming a more convenient and transparent mode of sale, insurance companies have now launched online plans which can be purchased by customers.
In no way does it compromise the quality of the product or its servicing.