In the Bellman-Ford Algorithm, the principle of "Good news travels fast but bad news travels slow" is implemented. So if the cost of the link between two routers is increased, then the increase in cost is not shared quickly. Assuming that the cost between two routers has increased and the routers have yet to update the new cost, can we still transfer packets between the two routers?
can we still transfer packets between the two routers?
Yes. But your network might not work efficiently or at all.
Basically, most routing algorithms in practice use Dijkstra's algorithm (OSPF, IS-IS, SPB) which is faster to converge.
Any router can only use the information that is has gained access to - effectively, until the network has converged, there's no consistent information base and possibly even routing loops can exist.
Of course, you can still transfer/forward packets between routers before that happens - a routing protocol (that would use Bellmann-Ford) doesn't route, but it exchanges routing information to update the routing tables.
However, the whole network might not work consistently before it has fully converged. Therefore, fast convergence is key, so Dijkstra is preferred mostly.