That's easy enough to calculate. if the average drop rate is 2.5 per run you'll need 2k runs equalling 200 refills. If your runtime including loading screens (which takes a long time at least for me) is 1 minute you can achieve it in 1.38 days when running constantly. Though I believe the drop rate is lower.
With 1.8 frags per run you'll need 2778 runs => 278 refills taking 1.92 days. So yea. it's possible. The better question is, is it worth it ? That's even easier to answer: NO !
That being said, I like the idea of being able to spend your excess fragments. You don't have to, it's optional. And you don't need to spend en masse. If you're missing just 50 talisman frags to complete a cosmic it may be worth some grinding.