It is still undecidable. Pick some algorithm M that has a time complexity dependent on the input (whatever exactly that means).
Now given some Turing machine T, consider the algorithm A that works as follows:
1) Simulate T on empty input until it halts.
2) Run M on the original input.
If T does not halt, then A never halts for any input, hence has time complexity independent of the input. If T halts after k steps, then A essentially takes k steps more than M does for any input. Since M's time complexity depends on the input, so should the time complexity of A.