Yes you definitely can. It is commonly called ETF arbitrage and very competitive and requires high frequency trading infrastructure.
How would you place an order of two legs? which leg to be Long and which to be short? and when ? at cross over?
Since these pairs have an inverse leverage relationship you would buy/buy or sell/sell, not buy/sell etc. The goal is to have zero exposure to the ETF index (in this case the SP500). How to execute this trade is sort of a complicated question, but the short answer is that it requires HFT capabilities.
Keep in mind these all return whatever multiple of the daily return of the underlying index. So set up a spreadsheet to see what this means with some dummy index returns. Basically after 1 day the two positions are going to be unbalanced, so especially with a 3x you're going to have to rebalance your position daily.
Personally I think ETFs are excellent Spread Trade vehicles. IMO the best use of an ETF is to short a dog or buy a star Company versus the appropriate sector ETF. Both positions should be weighted by valuation-adjusted volatility.
They definitely do allow for many possibilities when moving to a stat arb type trade as you describe. However, the trade described in the OP is not really feasible for a retail investor.
I personally would NOT daytrade an ETF pair / I am referring to a swing trade over a period of days, weeks, even months if its performing.
its not silly at all. better to trade this in a swing format imho once u understand how it moves. you equalize the spread by buying different share amounts but the same dollar amount of each etf or stock.