If the stock market comes crashing down as some predict,
Firstly the stock markets are regulated by some organizations and you would not see a crashing unless a diasater of the entire planet occurs, this pandemic is much less in its impact.
what will you do with your alt coins? Swap them for BTC?
You still havent sold your altcoins for BTC? This was the time to sell them at profit though. No one know when you will see 60k+ USD/BTC again.
I know that many view BTC as a safe haven (like digital gold) but historically, BTC prices have been positively correlated with the stock market.
These two do not have a proven connection. The correlation data is anecdotal and often biased from person to person. Precious metals, stock, crypto all seem to move in different directions depending on the situation.
That said, in the case of an actual market crash, I think BTC could act like digital gold and appreciate since it's now more widely accepted as a "real thing" than ever...
Bitcoin is not widely accepted yet. Most countries where it is accepted, good for them but there are several more where it is either illegal or a grey area. This will change with time but the concept of digital gold is a wrong one and more of an apples and oranges comparison.
Both gold and bitcoin have their pros and cons. Dividing money among both would be an intelligent approach. Bitcoin bulls want you to sell your gold to buy bitcoin so they can sell. Dont fall for that trap.