No, not for all algorithms. The following test in R2014b confirms this.
>> C=speye(3); d=sparse([3;2;1]); A=C; b=d; lsqlin(C,d,A,b)
Warning: The trust-region-reflective algorithm can handle bound constraints only;
using active-set algorithm instead.
> In lsqlin at 304
Warning: Cannot use sparse matrices with active-set algorithm: converting to full.
> In lsqlin at 353
Optimization terminated.
ans =
3
2
1
The strange thing, however, is that in R2013b, the active-set algorithm handles sparse input just fine, or at least it does not return a warning as above,
>> C=speye(3); d=sparse([3;2;1]); A=C; b=d; lsqlin(C,d,A,b,[],[],[],[],[],optimoptions(@lsqlin,'Algorithm','active-set'))
Optimization terminated.
ans =
3
2
1
