Is sealing a leak from the inside of my roof a bad idea?
You will save money by fixing the roof properly from the top-side. 

A bottom up repair has almost no chance of working. On the contrary, it has a high probability of moving the leak to somewhere less visible, which has a high likelihood of causing expensive future damage. (Damage that's usually found in a home inspection prior to sale, which will either need remediation or reduced price. Don't even get me started on the damage to the future sale that occurs when the word 'mold' appears on an inspection report.)