Can Alt Coins (~3 months) after ICO actually outgrow BTC in the long-run?

[RonRico]

I'm fairly new to this space but this is something I've been trying to understand for several months.  In the long-run, as long as BTC is used as a base to convert altcoins to fiat, can alt-coins surpass the growth rate of bitcoin?  I find that hard to believe because BTC is always being used as the base to trade in and out of non-coinbase alts.  On days like today I'm seeing BTC regain strength while altcoins are falling in comparison.  But when BTC falls most altcoins fall even harder.  I feel like unless there is a huge news driven event that pushes an altcoin higher, BTC will eventually catch up in the long run until the fiat conversion dynamic changes.