Will Bloomberg Composite Crude Oil Subindex rise when Crude oil prices rise?

1) Will this index rise when and if oil price rises?

Yes, this index would have a positive impact from an increase in oil prices but there are other factors at play (see below)

2) Does this index decay over long term?

Potentially, and in the current environment, yes. The oil markets are in a very well defined contango term structure which means that nearer term contracts (which these funds buy) are cheaper than longer term contracts. Every month when its time to roll out of expiring contracts, they would have to sell something cheap to buy something more expensive which has a negative effect on yield and causes some drift in tracking the underlying.

Other factors to consider are the very fluid dynamics in the oil markets at the moment. The current scarcity of storage implies that contango will be around for a while as a way for the market to incentivize storage holders to mop up excess supply. Negative prices might have been a one time thing or something that could recur to the detriment of funds like this that have to get out of usually sizable financial positions.

USO (another oil ETF) has been in the news for changing fund rules multiple times in a bid to survive, and for the CME clamping down on positions they can hold given their heightened risk profile in this environment. While this is a totally different fund, i noticed that its historical returns, are quite similar to that of USO, and one has to think of how similarly exposed they might be.

If i were in your shoes, i'd think of a different trade to effect a bullish point of view on oil without using an ETF.