Should Crypto-Prices Converge If One Exchange Has Positive Funding Rate While Another Has Negative?

I was revisiting the theory behind Deribit/Bitmex/Bybit ETH/BTC funding rate arbitrager. Given the theory behind funding rates, if one exchange has a negative rate while another has positive it should mean that the prices converge.

Positive: longs pay shorts

Negative: shorts pay longs

if Exchange A is Positive and Exchange C is Negative, it implies:

1. A is 'too long' vs spot, meaning price should go down

2. C is 'too short' vs spot, meaning price should go up

A Hedged Position Across These Two Would Have The Following Implications:

1. A short on A would net funding revenues

2. A short on A would gain value as the price comes closer to spot

3. A long position on C would net funding revenues

4. A long position on C would gain value as the price comes closer to spot

Herein, funding arbitrage has a secondary layer of earnings from the convergence of perpetuals.

The function of the bot would include limit ordering into relative position based on % of rate +/-, or the difference in absolute value.

Otherwise, in such cases, it has another secondary revenues' layer by earning maker rebates both getting into position (while relatively hedged) but also at the top of the exposure as it continues to trade within the maximum skew and earn maker rebates.