Yes, that will work, but there is an EASY way to do that.
SPLITTERS and HUBS are the two types of devices that can be used to connect several fans to a single mobo header. Those two differ in one very important way. A SPLITTER simply connects all its fans in parallel to the header, and draws ALL power for its fans from that header. It has only two types of connection "arms": one female connector to the mobo header, and several output male connectors for fans to plug in. A typical mobo fan header can supply up to 1.0 A max current to its total connected load (YOUR mobo header may be different), and that limits what a Splitter can allow. But a Splitter CAN be used for either 3-pin or 4-pin fans.
A HUB is a different device that may look at lot the same as a Splitter. But BEWARE - many makers mis-label these two device types and use both terms as if they mean the same thing! A HUB has those same two types of connectors - one to a header, and several to fans - PLUS is has one extra "arm" or connection point that must connect to a power output from the PSU - typically, an unused SATA power output connector. The HUB connects all its fans to the power from the PSU (+12 VDC and Ground) and draws none from the host header, so the header's limit does not apply. The limit of the power from the SATA connection to the Hub and its fans is 4.5 A max total. The Hub then shares the PWM signal from Pin #4 of the host header to all the fans, but this does NOT overload that signal source and does not limit how many fans can be used this way. The restriction of a HUB is that it must be used with a mobo header that actually DOES use the 4-pin PWM Mode of control, AND it can be used only with 4-pin PWM-type fans.
So, a common commercial fan HUB will do exactly what you ask. It sends the PWM signal from a host header to all the fans, but it provides those fans with power from the PSU, drawing none from the header. Examples of fan Hubs:
That looks like a collection of cable arms, but NOTE that one of those arms goes to a SATA power output from the PSU, and one goes to a mobo header.
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That looks like a circuit board with ten output connectors along its edges and one connector at one end for a cable to a mobo header. It has another connector on the board end where you plug in that SATA power connector.
That looks like a closed box with portholes along both sides, but it, too, has cables to connect to a mobo fan header and a SATA power connector.
Any mobo header can deal with the speed signal coming back to it from only ONE fan. So each of these Hubs will return to the host header the speed signal of ONLY the one fan plugged into the specially-marked output port. On the "collected arms" style that is the only output with all 4 pins in it. On others it may be coloured, or labelled some special way, or simply "Port #1", or maybe "CPU FAN". When you are using the Hub for case ventilation fans only, connect it to a mobo SYS_FAN or CHA_FAN header and NOT to the CPU_FAN header, and then do NOT plug into that special port of the hub your CPU cooling fan. Just plug in there one of your case fans.
An important second function of any fan header is to monitor the speed signal returned to it from its fan for FAILURE - that is, no fan speed signal. A failure will pop up on your screen a warning so you can deal with that. However, when you use a Splitter or a Hub that cannot send back the speed signals of ALL its fans, those cannot all be monitored for failure. So from time to time YOU must check whether all your fans are still working.
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