Short answer first: yes — the CX-520D does add only a very small insertion loss (~0.2 dB) at L-band, so if the LNA is mounted at the antenna (mast/head) the CX-520D in front of the LNA produces a modest noise penalty (~+0.17–0.2 dB → ~+13 K to +20 K equivalent noise temperature).
But if the LNA is in the shack and you put the relay and/or 10 m of KMR-240 before the LNA, the loss of the 10 m feeder (≈3.1 dB for LMR-240/KMR-240 at ~1.42 GHz) dominates and will dramatically degrade sensitivity (system NF jumps to ≈3.5–3.7 dB and Trec → a few hundred K).

I computed the numbers below step-by-step using the SAWbird H1 datasheet, the CX-520D relay specs and LMR-240/KMR-240 attenuation charts. Sources: Nooelec SAWbird datasheet, Tohtsu/CX-520D product specs, Times/LMR-240 datasheet.

What I used (specs)

• Nooelec SAWbird+ H1 (datasheet): NF = 0.8 dB (typ), Gain ≈ 42 dB, Noise temp ≈ 59 K.
• Tohtsu CX-520D (datasheet/listings): Insertion loss ≈ 0.20 dB (≤0.20 dB in the 1.0–1.5 GHz region), isolation and VSWR OK for L-band. (The DX Shop Limited)
• KMR-240 (treated equivalent to LMR-240): attenuation ≈ ~31–32 dB/100 m at ~1.42 GHz → ≈0.31 dB/m → ≈3.1 dB for 10 m. (LMR-240 datasheet table used as proxy for KMR-240.) (timesmicrowave.com)

How I calculated (brief)

I used Friis cascade / passive-loss rules: a passive loss L (dB) placed before the first active amplifier multiplies the source and produces an increase in system noise roughly equal to that loss in dB. Conversions were done with F = 10^(NF/10) and Trec = (F − 1)·290 K. (I ran the arithmetic exactly to avoid rounding errors.)

Results — three realistic scenarios

1. Relay placed at mast, LNA also at mast (relay before LNA only)
   • Loss before LNA: relay ≈ 0.20 dB.
   • System NF → ≈0.97 dB (was 0.8 dB).
   • Equivalent receiver noise temperature → ≈72 K (was ≈59 K).
   • Interpretation: small, measurable hit (~+0.17 dB NF / +13 K). Acceptable for many amateur hydrogen-line setups; not catastrophic. (Good option if you must switch at the feed.) (The DX Shop Limited)
2. LNA in the shack, 10 m KMR-240 feedline before the LNA (no relay before LNA)
   • Loss before LNA: coax ≈ 3.10 dB (10 m).
   • System NF → ≈3.51 dB.
   • Equivalent receiver noise temperature → ≈361 K.
   • Interpretation: huge degradation — you lose most of the benefit of the low-NF LNA by putting it behind 10 m of KMR/LMR-240.
3. LNA in the shack, and you put CX-520D in front of LNA (coax + relay before LNA)
   • Loss before LNA: coax + relay ≈ 3.30 dB.
   • System NF → ≈3.69 dB.
   • Equivalent receiver noise temperature → ≈389 K.
   • Interpretation: worse than case 2 by a little — relay adds a small extra hit on top of the big coax loss.

(Those numeric results are the precise calculations I ran from the datasheet numbers above. I can show the exact arithmetic if you want it line-by-line.)

Practical takeaways / recommendations

• If your LNA is already at the mast (recommended): using the CX-520D immediately in front of the SAWbird gives only a small NF penalty (~+0.17–0.2 dB). That is usually acceptable if you need the antenna↔load switching and you take care of weatherproofing and contact health. The CX-520D’s specs show this is within its intended band. (The DX Shop Limited)
• If your LNA is in the shack (not recommended for sensitive H-line work): do not place the relay and the 10 m KMR-240 before the LNA — the feeder loss (~3.1 dB) will swamp the LNA’s performance and ruin sensitivity. Mount the LNA at the mast/head if at all possible. (timesmicrowave.com)
• If you cannot place the LNA at the mast and must do switching in the shack: consider doing the reference switching after the LNA where it won’t add to front-end NF (but you’ll lose a “true” antenna-terminated reference — you can calibrate differently). Alternatively use a noise-diode injection via directional coupler (inject a known noise after the LNA and correct in software) — that avoids introducing big pre-LNA loss.

Other considerations

• Mechanical relays age and contacts can become slightly lossy or corroded — check insertion loss occasionally with a VNA. Weatherproofing at the mast is crucial. (The DX Shop Limited)
• Relay isolation is good on the CX-520D (tens of dB at 1–1.5 GHz) so leakage isn’t usually a problem for routine cal switching. (The DX Shop Limited)