Control cuts, also called control joints, are used to control the movement of concrete and prevent cracking. Sealing them and then laying tile over sealed concrete could have disastrous effects. The sealed concrete won't be able to flex, and will either crack under the tile, delaminating it, or will cause the tile itself to crack.
Control cuts made by contractors are saw cut and are generally flush on each side. They don't exhibit the unevenness of random cracking and so they won't cause an uneven tile surface. Uneven tile surfaces can result in a rolling, "hilly" floor. It can also result in a poor adhesive bond and tiles that come delaminated, or unglued. Tiles installed on an uneven surface may even crack as the adhesive they are glued down with dries.
Any crack in concrete can allow moisture to seep to the surface. Moisture can crack or delaminate tiles. If moisture is a problem, consider caulking your control cuts with a silicone caulk product. These products are flexible enough to allow the concrete to move. They are also water-resistant and won't peel away from the concrete if they get wet.
Installing tile directly onto concrete is risky. Tile and concrete expand and contract at different rates, leading to cracking or even delaminating. Lay 1/4-inch plywood over the concrete sub-floor and secure it with 1-1/4-inch underlayment nails for best results. Anti-fracture membranes are also available, which can help reduce the stress of concrete movement on tile.