Yes, the mark prices of contracts within the same contract type can vary, which can lead to a loss in one contract that is not covered by a corresponding gain in another contract, resulting in a potential liquidation if the loss in one contract brings the portfolio value below maintenance margin.
The premium/discounts vary across maturities. The maximum premium/discount from the index price for perpetual derivatives contracts is 1% and the maximum premium/discount from the index price for fixed maturities is 20% at 210 days-to-maturity and 1% with 1 day to maturity and linearly interpolated in between.
For example, the Bitcoin Real Time Index (BRTI) is currently 35,000 and a trader has a short position in the perpetual contract and a long position in the fixed maturity, each with varying entry prices. In the fixed contract, there are ~87 days left to maturity, meaning that the mark price in the fixed market can drift as far away as ~8.82% from the index price (down to 31,913 or up to 38,087), whereas the perpetual contract can only drift as far away as 1% from the index price (down to 34,650 or up to 35,350).
If the price on the fixed contract dropped enough to bring the portfolio value below maintenance margin (even if the perpetual position was in profit), then all of the positions in that margin account would be liquidated. When managing risk on spread positions, it is important to account for these premium variations.