No, it’s the opposite. When base salary is converted to a signing bonus, it lowers the cap hit in the current year, and increases cap hits in future years - and therefore if he were cut in a future year, his dead money hit increases.
That’s why teams tend to be careful with these restructurings — ideally, you’d use it only for players that you don’t expect to be cut prior to the end of the contract. If you do it for everyone, you’ll wind up either 1) keeping players who stink, producing poorer on-field results, or 2) cutting them and taking large dead cap hits, leading to “cap hell” for that year as you can’t really maneuver. An increasing cap and very strong drafting can counterbalance that (part of how the Saints have done this while still staying competitive through the years).