Can I directly synthesize oligos with sticky ends rather than doing a restriction digest?
Yes, you can design your oligonucleotides with the desired overhangs and ligate them directly into a digested vector.
If you order the oligos with the desired overhangs, you may wish to add a 5' phosphorylation modification to annealed oligos prior to ligating into your digested vector to increase the ligation efficiency.
You can order the oligos with the modification or perform a phosphorylation reaction to your oligos after receiving them. When you digest your vector with a restriction enzyme, the restriction enzyme will leave a 5' phosphorylation on the vector overhangs that will allow the oligo overhangs to be ligated into the vector.